P is a point on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ . The in-radius of ΔPSS’ (S and S’ are focii), where its area is maximum.

a common tangent is a line that is a tangent to more than one curves..

If F₁and F₂are the feet of the perpendiculars from the foci S₁& S₂of an ellipse $fraction numerator x to the power of 2 end exponent over denominator 5 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 3 end fraction equals 1$ on the tangent at any point P on the ellipse, then (S₁F₁). (S₂F₂) is equal to-

selecting a point on the major axis provides an ease of calculation.

If F₁and F₂are the feet of the perpendiculars from the foci S₁& S₂of an ellipse $fraction numerator x to the power of 2 end exponent over denominator 5 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 3 end fraction equals 1$ on the tangent at any point P on the ellipse, then (S₁F₁). (S₂F₂) is equal to-

selecting a point on the major axis provides an ease of calculation.

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 and 25x² + 9y² = 450 passing through (3 , 5) is

if a point lies inside, no real tangents can be drawn from the point on the curve. on the curve, then only 1 tangent and if outside, then 2 tangents can be drawn.

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 and 25x² + 9y² = 450 passing through (3 , 5) is

if a point lies inside, no real tangents can be drawn from the point on the curve. on the curve, then only 1 tangent and if outside, then 2 tangents can be drawn.

P is a variable point on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction$ + $fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction$ = 1 with AA' as the major axis. Then, the maximum value of the area of the triangle APA' is-wor

when we differentiate an expression, we get the critical points where either maxima or minima can exist.

P is a variable point on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction$ + $fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction$ = 1 with AA' as the major axis. Then, the maximum value of the area of the triangle APA' is-wor

when we differentiate an expression, we get the critical points where either maxima or minima can exist.

A man running round a race course, notes that the sum of the distances of two flag-posts from him is always 10 meters and the distance between the flag- posts is 8 meters. The area of the path he encloses in square metres is-

If C is the centre of the ellipse 9x² + 16y² = 144 and S is one focus. The ratio of CS to major axis, is

If any tangent to the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ intercepts equal lengths $ell$ on the axes, then $ell$ =

The line x = at² meets the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ in the real points if

The length of the common chord of the ellipse $fraction numerator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent over denominator 9 end fraction plus fraction numerator left parenthesis y minus 2 right parenthesis to the power of 2 end exponent over denominator 4 end fraction equals 1$ and the circle (x –1)²+ (y –2)² = 1 is

maths-

The locus of extremities of the latus rectum of the family of ellipses b²x² + y² = a²b² is

maths-General

If A, A' are the vertices S, S' are the focii and Z, Z' are the feet of the directrix of an ellipse then A'S, A'A, A'Z are in

The tangent at any point on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ meets the tangents at the vertices A, A' in L and L'. Then AL. A'L' =

the lines parallel to the y axis are pf the form x=a since the y intercept is undefined.

The tangent at any point on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ meets the tangents at the vertices A, A' in L and L'. Then AL. A'L' =

the lines parallel to the y axis are pf the form x=a since the y intercept is undefined.

The circle on SS' as diameter intersects the ellipse in real points then its eccentricity (where S and S'are the focus of the ellipse)

The circle on SS'as diameter touches the ellipse then the eccentricity of the ellipse is (where S and S'are the focus of the ellipse)

The tangent at P on the ellipse meets the minor axis in Q, and PR is drawn perpendicular to the minor axis and C is the centre. Then CQ . CR =