MEDIUM
JEE Main
IMPORTANT
Earn 100

The ratio of the area enclosed by the locus of the midpoint of PS and area of the ellipse is (P be any point on the ellipse and S is its focus)

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Important Questions on Ellipse

HARD
JEE Main
IMPORTANT
Number of integral values of α for which the point 7-54α, α lies inside the ellipse x225+y216=1 is
HARD
JEE Main
IMPORTANT
Coordinates of the vertices B and C of a triangle ABC are 2,0 and 8,0, respectively. The vertex A is varying in such a way that 4tanB2·tanC2=1. Then locus of A is
HARD
JEE Main
IMPORTANT
PQ and QR are two focal chords of an ellipse and the eccentric angles of P, Q and R are 2α,2β and 2γ respectively, then tanβtanγ is
HARD
JEE Main
IMPORTANT

In triangle ABC, a=4 and b=c= 22. A point P moves within the triangle such that the square of its distance from BC is half the area of rectangle contained by its distances from the other two sides. If D is the centre of locus of P, then

HARD
JEE Main
IMPORTANT

Extremities of the latus rectum of the ellipse x2a2+y2b2=1a>b having a major axis 2a lies on:

HARD
JEE Main
IMPORTANT
Identify correct statement(s) about conic x-52+y-72+x+12+y+12=12
MEDIUM
JEE Main
IMPORTANT
The value of λ, for which the line 2x-83 λy=-3 is a normal to the conic x2+y24=1 is :
HARD
JEE Main
IMPORTANT
If the length of portion of the major axis intercepted between the tangent and normal at a point Pacosθ,bsinθ on the ellipse x2a2+y2b2=1 is equal to the length of semi-major axis, then eccentricity of the ellipse is