HARD
JEE Main
IMPORTANT
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The chords of contact of perpendicular tangents to the ellipse x2a2+y2b2=1 touch another fixed ellipse whose equation is

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Important Questions on Ellipse

MEDIUM
JEE Main
IMPORTANT
The second-degree equation x2+4y2+2x+16y+13=0 represents
MEDIUM
JEE Main
IMPORTANT
In the standard ellipse, the lines joining the ends of the minor axis to one of the focus are at right angles. The distance between the focus and the nearer vertex is 10-5. The equation of the ellipse is
MEDIUM
JEE Main
IMPORTANT
The foci of an ellipse are -2,4 and 2,1. The point 1,236 is an extremity on the minor axis. What is the value of the eccentricity?
MEDIUM
JEE Main
IMPORTANT
Let Q=3, 5 and R=7,35. A point P in the XY-plane varies in such a way that perimeter of PQR is 16. Then the maximum area of PQR is
MEDIUM
JEE Main
IMPORTANT
The eccentricity of the ellipse x-32+y-42=y29 is
HARD
JEE Main
IMPORTANT
An area is bounded by the circle which is concentric with the ellipse x225+y29=1 and which passes through the point 4,-95, the vertical chord common to both circle and ellipse on the positive side of x-axis is
EASY
JEE Main
IMPORTANT
If A and B are foci of the ellipse x-2y+32+8x+4y+42=20 and P is any point on it, then PA+PB=
HARD
JEE Main
IMPORTANT
The distance between the directrices of the ellipse (4x-8)2+16y2=(x+3y+10)2 is