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Maths-

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Question

Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐

$(\frac{4}{3}, \frac{3}{4})$
$(\frac{3}{4}, \frac{3}{4})$
$(1, 1)$
$(1, \frac{4}{3})$

The correct answer is: $left parenthesis 1 comma blank fraction numerator 4 over denominator 3 end fraction right parenthesis$

Related Questions to study

The locus of the centres of the circles which cut the circles $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 6 y plus 9 equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 5 x plus 4 y minus 2 equals 0$ orthogonally is ‐

The locus of the centres of the circles which cut the circles $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 6 y plus 9 equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 5 x plus 4 y minus 2 equals 0$ orthogonally is ‐

The centre of the smallest circle touching the circles $x squared plus y squared minus 2 y minus 3 equals 0$ and $x squared plus y squared minus 8 x minus 18 y plus 93 equals 0$ is

The centre of the smallest circle touching the circles $x squared plus y squared minus 2 y minus 3 equals 0$ and $x squared plus y squared minus 8 x minus 18 y plus 93 equals 0$ is

Statement -I : If – 2h = a + b, then one line of the pair of lines $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ bisects the angle between co-ordinate axes in positive quadrant.
Statement -II : If ax + y(2h + a) = 0 is a factor of $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ then b + 2h + a = 0.

Statement -I : If – 2h = a + b, then one line of the pair of lines $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ bisects the angle between co-ordinate axes in positive quadrant.
Statement -II : If ax + y(2h + a) = 0 is a factor of $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ then b + 2h + a = 0.

parallel

P is point on either of the two lines $y minus square root of 3 vertical line x vertical line equals 2$ at a distance of 5 units from their point of intersection. The co-ordinates of the foot of the perpendicular from P on the bisector of the angle between them are :-

P is point on either of the two lines $y minus square root of 3 vertical line x vertical line equals 2$ at a distance of 5 units from their point of intersection. The co-ordinates of the foot of the perpendicular from P on the bisector of the angle between them are :-

$alpha comma blank beta$ are the roots of the equation $x squared minus 3 x plus A equals 0$ and $gamma comma delta$ are the roots of the equation $x squared minus 12 x plus B equals 0. I f alpha comma beta comma gamma comma delta$ form an increasing GP, then $left parenthesis A comma blank B right parenthesis$ is equal to

$alpha comma blank beta$ are the roots of the equation $x squared minus 3 x plus A equals 0$ and $gamma comma delta$ are the roots of the equation $x squared minus 12 x plus B equals 0. I f alpha comma beta comma gamma comma delta$ form an increasing GP, then $left parenthesis A comma blank B right parenthesis$ is equal to

The sum of the series $1 times n plus 1 plus 2 times open parentheses n minus 1 close parentheses plus 3 times open parentheses n minus 2 close parentheses horizontal ellipsis plus n times 1$ is

The sum of the series $1 times n plus 1 plus 2 times open parentheses n minus 1 close parentheses plus 3 times open parentheses n minus 2 close parentheses horizontal ellipsis plus n times 1$ is

parallel

The sum of the series $1 times 2 times 3 plus 2 times 3 times 4 plus 3 times 4 times 5 plus...$ to $n$ terms is

The sum of the series $1 times 2 times 3 plus 2 times 3 times 4 plus 3 times 4 times 5 plus...$ to $n$ terms is

If the sum of an infinite GP and the sum of square of its term is 3, then the common ratio of the first series is

If the sum of an infinite GP and the sum of square of its term is 3, then the common ratio of the first series is

If $a$ and $b$ are two different positive real numbers, then which of the following relations is true

If $a$ and $b$ are two different positive real numbers, then which of the following relations is true

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If $A subscript 1 end subscript comma blank A subscript 2 end subscript$ are two A $blank times$ M’s between $a$ and $b$ and $G subscript 1 end subscript comma blank G subscript 2 end subscript$ are two GM’s between $a$ and $b$ then $fraction numerator A subscript 1 end subscript plus A subscript 2 end subscript over denominator G subscript 1 end subscript G subscript 2 end subscript end fraction$ is

If $A subscript 1 end subscript comma blank A subscript 2 end subscript$ are two A $blank times$ M’s between $a$ and $b$ and $G subscript 1 end subscript comma blank G subscript 2 end subscript$ are two GM’s between $a$ and $b$ then $fraction numerator A subscript 1 end subscript plus A subscript 2 end subscript over denominator G subscript 1 end subscript G subscript 2 end subscript end fraction$ is

the sum of $n$ terms of the infinite series $1 times 3 squared plus 2 times 5 squared plus 3 times 7 squared plus... infinity$ is

the sum of $n$ terms of the infinite series $1 times 3 squared plus 2 times 5 squared plus 3 times 7 squared plus... infinity$ is

The value of $a to the power of log subscript b end subscript invisible function application x end exponent comma$ where $a equals 0.2 comma blank b equals square root of 5 comma$ $x equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 8 end fraction plus fraction numerator 1 over denominator 16 end fraction plus... infinity comma$ is

The value of $a to the power of log subscript b end subscript invisible function application x end exponent comma$ where $a equals 0.2 comma blank b equals square root of 5 comma$ $x equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 8 end fraction plus fraction numerator 1 over denominator 16 end fraction plus... infinity comma$ is

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The number 111…1 (91 times) is a/an

The number 111…1 (91 times) is a/an

Number of identical terms in the sequence 2, 5, 8, 11,… upto 100 terms and 3, 5, 7, 9, 11,… upto 100 terms, are

Number of identical terms in the sequence 2, 5, 8, 11,… upto 100 terms and 3, 5, 7, 9, 11,… upto 100 terms, are

If $e to the power of e to the power of x end exponent end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus horizontal ellipsis$ , then

If $e to the power of e to the power of x end exponent end exponent equals a subscript 0 end subscript plus a subscript 1 end subscript x plus a subscript 2 end subscript x to the power of 2 end exponent plus horizontal ellipsis$ , then

parallel

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