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An ellipse has the point $left parenthesis 1 comma blank minus 1 right parenthesis blank$ and $left parenthesis 2 comma blank minus 1 right parenthesis blank$ as its foci and $x plus y equals 5$ as one of its tangent then the coordinate of the point where this line touches the ellipse are

$(\frac{34}{9} \frac{11}{9})$
$(\frac{32}{9} \frac{13}{9})$
$(- \frac{34}{9} \frac{79}{9})$
$(- \frac{32}{9}, \frac{77}{9})$

The correct answer is: $left parenthesis fraction numerator 34 over denominator 9 end fraction fraction numerator 11 over denominator 9 end fraction right parenthesis$

Given- An ellipse has the point $left parenthesis 1 comma blank minus 1 right parenthesis blank$ and $left parenthesis 2 comma blank minus 1 right parenthesis blank$ as its foci and $x plus y equals 5$ as one of its tangent then we have to find the coordinate of the point where this line touches the ellipse.
$E q u a t i o n space o f space tan g e n t space i s space x plus y minus 5 equals 0. F o c i space o f space e l l i p s e space a r e space left parenthesis 1 comma negative 1 right parenthesis space a n d space left parenthesis 2 comma negative 1 right parenthesis. P r o d u c t space o f space p e r p e n d i c u l a r space f r o m space f o c i space u p o n space a n y space tan g e n t space i s space e q u a l space t o space s q u a r e space o f space t h e space s e m i space m i n o r space a x i s. T h u s space open vertical bar fraction numerator 1 minus 1 minus 5 over denominator square root of 1 plus 1 end root end fraction close vertical bar open vertical bar space fraction numerator 2 minus 1 minus 5 over denominator square root of 1 plus 1 end root end fraction close vertical bar space equals space b squared space b squared equals fraction numerator 5 cross times 4 over denominator 2 end fraction equals 10 D i s tan c e space b e t w e e n space f o c i equals 2 a e equals square root of left parenthesis 1 minus 2 right parenthesis squared plus left parenthesis negative 1 minus left parenthesis negative 1 right parenthesis right parenthesis squared end root a e equals 1 half left parenthesis a e right parenthesis squared equals fraction numerator 1 over denominator 4 end fraction a squared left parenthesis 1 minus b squared over a squared right parenthesis equals 1 divided by 4. a squared minus b squared equals 1 fourth a squared minus 10 equals 1 fourth a squared equals 41 over 4 C e n t r e space o f space t h e space e l l i p s e space i s space t h e space m i d space p o i n t space o f space f o c i. T h e r e f o r e comma space c e n t e r space i s space left parenthesis space space 3 over 2 space comma negative 1 right parenthesis. T h e r e f o r e comma space t h e space e q u a t i o n space o f space e l l i p s e space i s fraction numerator open parentheses x minus begin display style 3 over 2 end style close parentheses squared over denominator open parentheses begin display style 41 over 4 end style close parentheses end fraction plus left parenthesis y minus 1 right parenthesis squared over 10 equals 1 fraction numerator left parenthesis 2 x minus 3 right parenthesis over denominator 41 end fraction squared plus left parenthesis y plus 1 right parenthesis squared over 10 equals 1 S u b s t i t u t i n g space x space f r o m space t h e space e q u a t i o n space o f space tan g e n t comma space w e space h a v e space left parenthesis 2 left parenthesis 5 minus y right parenthesis minus 3 right parenthesis squared over 41 plus left parenthesis y plus 1 right parenthesis squared over 10 equals 1 left parenthesis 7 minus 2 y right parenthesis squared over 41 plus left parenthesis y plus 1 right parenthesis squared over 10 equals 1 10 left parenthesis 49 plus 4 y squared minus 28 y right parenthesis plus 41 left parenthesis y squared plus 1 plus 2 y right parenthesis equals 410 490 plus 40 y squared minus 280 y plus 41 y squared plus 41 plus 82 y equals 410 81 y squared minus 198 y plus 121 equals 0 left parenthesis 9 y minus 11 right parenthesis squared equals 0 y equals 11 over 9 N o w comma space x plus y minus 5 equals 0 x equals 5 minus y x equals 5 minus 11 over 9 x equals 34 over 9 S o comma space t h e space p o i n t space o f space c o n t a c t space o f space tan g e n t space t o space e l l i p s e space i s space open parentheses 34 over 9 comma 11 over 9 close parentheses. E l l i p s e space a l s o space p a s s e s space t h r o u g h space t h i s space p o i n t. space$

So, the point of contact of tangent to ellipse is $S o comma space t h e space p o i n t space o f space c o n t a c t space o f space tan g e n t space t o space e l l i p s e space i s space open parentheses 34 over 9 comma 11 over 9 close parentheses.$ .

The arrangement of the ellipses in ascending order of their eccentricities when $open floor S B S to the power of 1 end exponent close$ is given, Where S & $S to the power of 1 end exponent$ are foci& $B$ is one end of the minor axis A) $open floor S B S to the power of 1 end exponent close equals 2 0 to the power of 0 end exponent$ B) $open floor S B S to the power of 1 end exponent close equals 6 0 to the power of 0 end exponent$ C) $open floor S B S to the power of 1 end exponent close equals 3 0 to the power of 0 end exponent$ D) $open floor S B S to the power of 1 end exponent close equals 9 0 to the power of 0 end exponent$

maths-General

General

maths-

$T h e p$ oints o $n t h e e$ llipse 3 $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 37 comma$ where the normals to it are perpendicular to $6 x plus 5 y minus 2 equals 0$ are

maths-General

General

maths-

$E subscript 1 end subscript equals fraction numerator x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 9 end fraction minus 1 equals 0 comma$ $C equals 0$ is a greatest circle incribed in $E subscript 1 end subscript$ and Greatest Ellipse $E subscript 2 end subscript$ is incribed in c = 0 If the eccentricities of $E subscript 1 end subscript comma E subscript 2 end subscript$ are equal then the minor axis of $E subscript 2 end subscript equals 0$ is

maths-General

General

physics-

Two thin lenses of focal lengths 1 f and 2 f are in contact and coaxial. The combination is equivalent to a single lens of power

physics-General

General

chemistry-

In which case first has higher solubility than second?
I) Phenol, Benzene
II) Nitrobenzene, Phenol
III) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehyde
IV) CH₃CHO, CH₃–O–CH₃
V) o–Nitrophenol, p–Nitrophenol
VI)

chemistry-General

General

maths-

If $alpha$ and $beta$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

maths-General

General

maths-

The point $left parenthesis a comma 2 a right parenthesis$ is an interior point of the region bounded by the parabola $y to the power of 2 end exponent equals 16 x$ and the double ordinate through the focus Then ‘a’ belongs to the open interval

maths-General

General

maths-

Through the vertex $O$ ofthe parabola $y to the power of 2 end exponent equals 4 a x$ chords OP, OQ are drawn at right angles to each other If the locus of mid points of the chord PQ is a parabola then its vertex is

maths-General

General

maths-

The area of the trapezium whose vertices lie on the parabola $y to the power of 2 end exponent equals 4 x$ and its diagonals pass through $left parenthesis 1 , 0 right parenthesis$ and having length $fraction numerator 25 over denominator 4 end fraction$ units each is

maths-General

General

maths-

The Locus of centre of circle which touches given circle externally and the given line is

maths-General

General

maths-

If the length of tangents from $left parenthesis a comma b right parenthesis$ to the circles $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 4 x minus 5 equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 6 x minus 2 y plus 6 equals 0$ are equal then $10 a minus 2 b equals$

maths-General

General

maths-

The line $2 x plus 3 y equals 1$ cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ in $P$ and Q Then the equation of the smaller circle passing through $P$ and $Q$

maths-General

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An ellipse has the point and as its foci and as one of its tangent then the coordinate of the point where this line touches the ellipse are

The correct answer is:

Given- An ellipse has the point and as its foci and as one of its tangent then we have to find the coordinate of the point where this line touches the ellipse.

Related Questions to study

The arrangement of the ellipses in ascending order of their eccentricities when is given, Where S & are foci& is one end of the minor axis A) B) C) D)

The arrangement of the ellipses in ascending order of their eccentricities when is given, Where S & are foci& is one end of the minor axis A) B) C) D)

oints ollipse 3where the normals to it are perpendicular to are

oints ollipse 3where the normals to it are perpendicular to are

is a greatest circle incribed in and Greatest Ellipse is incribed in c = 0 If the eccentricities of are equal then the minor axis of is

is a greatest circle incribed in and Greatest Ellipse is incribed in c = 0 If the eccentricities of are equal then the minor axis of is

Two thin lenses of focal lengths 1 f and 2 f are in contact and coaxial. The combination is equivalent to a single lens of power

Two thin lenses of focal lengths 1 f and 2 f are in contact and coaxial. The combination is equivalent to a single lens of power

Methanol and acetone can be separated by:

Methanol and acetone can be separated by:

Decreasing order of solubility of following compounds is:

Decreasing order of solubility of following compounds is:

Which of the following statement is correct about tropolone?

Which of the following statement is correct about tropolone?

In which case first has higher solubility than second?I) Phenol, BenzeneII) Nitrobenzene, PhenolIII) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehydeIV) CH3CHO, CH3–O–CH3V) o–Nitrophenol, p–NitrophenolVI)

In which case first has higher solubility than second?I) Phenol, BenzeneII) Nitrobenzene, PhenolIII) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehydeIV) CH3CHO, CH3–O–CH3V) o–Nitrophenol, p–NitrophenolVI)

If and are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

If and are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

The point is an interior point of the region bounded by the parabola and the double ordinate through the focus Then ‘a’ belongs to the open interval

The point is an interior point of the region bounded by the parabola and the double ordinate through the focus Then ‘a’ belongs to the open interval

Through the vertex ofthe parabola chords OP, OQ are drawn at right angles to each other If the locus of mid points of the chord PQ is a parabola then its vertex is

Through the vertex ofthe parabola chords OP, OQ are drawn at right angles to each other If the locus of mid points of the chord PQ is a parabola then its vertex is

The area of the trapezium whose vertices lie on the parabola and its diagonals pass through and having length units each is

The area of the trapezium whose vertices lie on the parabola and its diagonals pass through and having length units each is

The Locus of centre of circle which touches given circle externally and the given line is

The Locus of centre of circle which touches given circle externally and the given line is

If the length of tangents from to the circles and are equal then

If the length of tangents from to the circles and are equal then

The line cuts the circle in and Q Then the equation of the smaller circle passing through and

The line cuts the circle in and Q Then the equation of the smaller circle passing through and

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An ellipse has the point $left parenthesis 1 comma blank minus 1 right parenthesis blank$ and $left parenthesis 2 comma blank minus 1 right parenthesis blank$ as its foci and $x plus y equals 5$ as one of its tangent then the coordinate of the point where this line touches the ellipse are

The correct answer is: $left parenthesis fraction numerator 34 over denominator 9 end fraction fraction numerator 11 over denominator 9 end fraction right parenthesis$

$T h e p$ oints o $n t h e e$ llipse 3 $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 37 comma$ where the normals to it are perpendicular to $6 x plus 5 y minus 2 equals 0$ are

$T h e p$ oints o $n t h e e$ llipse 3 $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 37 comma$ where the normals to it are perpendicular to $6 x plus 5 y minus 2 equals 0$ are

In which case first has higher solubility than second?
I) Phenol, Benzene
II) Nitrobenzene, Phenol
III) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehyde
IV) CH₃CHO, CH₃–O–CH₃
V) o–Nitrophenol, p–Nitrophenol
VI)

In which case first has higher solubility than second?
I) Phenol, Benzene
II) Nitrobenzene, Phenol
III) o–Hydroxybenzaldehyde, p–Hydroxy benzaldehyde
IV) CH₃CHO, CH₃–O–CH₃
V) o–Nitrophenol, p–Nitrophenol
VI)

If $alpha$ and $beta$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

If $alpha$ and $beta$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

The point $left parenthesis a comma 2 a right parenthesis$ is an interior point of the region bounded by the parabola $y to the power of 2 end exponent equals 16 x$ and the double ordinate through the focus Then ‘a’ belongs to the open interval

The point $left parenthesis a comma 2 a right parenthesis$ is an interior point of the region bounded by the parabola $y to the power of 2 end exponent equals 16 x$ and the double ordinate through the focus Then ‘a’ belongs to the open interval

Through the vertex $O$ ofthe parabola $y to the power of 2 end exponent equals 4 a x$ chords OP, OQ are drawn at right angles to each other If the locus of mid points of the chord PQ is a parabola then its vertex is

Through the vertex $O$ ofthe parabola $y to the power of 2 end exponent equals 4 a x$ chords OP, OQ are drawn at right angles to each other If the locus of mid points of the chord PQ is a parabola then its vertex is

The area of the trapezium whose vertices lie on the parabola $y to the power of 2 end exponent equals 4 x$ and its diagonals pass through $left parenthesis 1 , 0 right parenthesis$ and having length $fraction numerator 25 over denominator 4 end fraction$ units each is

The area of the trapezium whose vertices lie on the parabola $y to the power of 2 end exponent equals 4 x$ and its diagonals pass through $left parenthesis 1 , 0 right parenthesis$ and having length $fraction numerator 25 over denominator 4 end fraction$ units each is

The line $2 x plus 3 y equals 1$ cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ in $P$ and Q Then the equation of the smaller circle passing through $P$ and $Q$

The line $2 x plus 3 y equals 1$ cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ in $P$ and Q Then the equation of the smaller circle passing through $P$ and $Q$