Normal to the ellipse `(x^2)/(64)+(y^2)/(49)=1` intersects the major and minor axes at `Pa n dQ` , respectively. Find the locus of the point dividing segment `P Q` in the ratio 2:1.

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at points Aa n dB , respectively. If C is the center of the ellipse, then find area of triangle A B Cdot

For the ellipse x^(2)+ 3y^(2) = a^(2) find the length of major and minor axis.

Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).

If the normal at any point P of the ellipse (x^(2))/(16)+(y^(2))/(9) =1 meets the coordinate axes at M and N respectively, then |PM|: |PN| equals

If normal at any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

Any ordinate M P of the ellipse (x^2)/(25)+(y^2)/9=1 meets the auxiliary circle at Qdot Then locus of the point of intersection of normals at Pa n dQ to the respective curves is (a) x^2+y^2=8 (b) x^2+y^2=34 (c) x^2+y^2=64 (d) x^2+y^2=15

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA' as the major axis. Find the maximum area of triangle A P A '