A point P lies on the ellipe 64(y−1)2+49(x+2)2=1 . If the distance of P from one focus is 10 units, then find its distance from other focus.
Normal to the ellipse 64x2+49y2=1 intersects the major and minor axes at PandQ , respectively. Find the locus of the point dividing segment PQ in the ratio 2:1.
If the normal at P(2,233) meets the major axis of ellipse 16x2+9y2=1 at Q , and S and S′ are the foci of the given ellipse, then find the ratio SQ:SprimeQ˙
Ois the origin & also the centre of two concentric circles having radii of the inner & the outer circle as
If the tangent at any point of the ellipse a3x2+b2y2=1 makes an angle α with the major axis and an angle β with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosαcosβ
If the line lx+my+n=0 cuts the ellipse (a2x2)+(b2y2)=1 at points whose eccentric angles differ by 2π, then find the value of n2a2l2+b2m2 .
If the area of the ellipse (a2x2)+(b2y2)=1 is 4π , then find the maximum area of rectangle inscribed in the ellipse.