MEDIUM
JEE Main
IMPORTANT
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Let x2a2+y2b2=1a>b be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, ϕt=512+t-t2, then a2+b2 is equal to :

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Important Questions on Ellipse

MEDIUM
JEE Main
IMPORTANT
Let x=4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 12. If P(1,β),β>0 is a point on this ellipse, then the equation of the normal to it at P is
MEDIUM
JEE Main
IMPORTANT
If the co-ordinates of two points A and B are (7,0) and  (-7,0) respectively and P is any point on the conic, 9x2+16y2=144, then PA+PB is equal to :
HARD
JEE Main
IMPORTANT
If the point P on the curve, 4x2+5y2=20 is farthest from the point Q0,-4, then PQ2 is equal to
HARD
JEE Main
IMPORTANT
Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x24+y22=1 from any of its foci?
 
MEDIUM
JEE Main
IMPORTANT
If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :
EASY
JEE Main
IMPORTANT
If the distance between the foci of an ellipse is 6 and the distance between its directrix is 12, then the length of its latus rectum is
MEDIUM
JEE Main
IMPORTANT
If 3x+4y=122 is a tangent o the ellipse x2a2+y29=1 for some aR, then the distance between the foci of the ellipse is
HARD
JEE Main
IMPORTANT
Let the line y=mx and the ellipse 2x2+y2=1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at -132,0 and 0,β, then β is equal to