If `(5,12)a n d(24 ,7)` are the foci of a hyperbola passing through the origin, then `e=(sqrt(386))/(12)` (b) `e=(sqrt(386))/(13)` `L R=(121)/6` (d) `L R=(121)/3`

If (5,12), (24,7) are the foci of the hyperbola passing through origin, then its eccentricity is

If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.

The radius of the circle passing through the foci of the ellipse (x^2)/(16)+(y^2)/9 and having its center (0, 3) is 4 (b) 3 (c) sqrt(12) (d) 7/2

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to (a) 3/7 (b) 2/7 (c) 5/7 (d) 3/5

A hyperbola is given with its vertices at (-2,0) and (2,0) one of the foci of hyperbola is (3,0) . Then which of the following points does not lie on hyperbola (A) (sqrt24,5) (B) (sqrt44, 5sqrt2) (C) (sqrt44, -5sqrt2) (D) (-6, 5sqrt2)

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). (a) sqrt(3) (b) sqrt(3)+1 ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). (a) sqrt(3) (b) sqrt(3)+1 (c) ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))

If a directrix of a hyperbola centred at the origin and passing through the point (4,-2 sqrt(3)) " is " 5x=4sqrt(5) and its eccentricity is e, then

The vertices of a parallelogram A B C D are A(3,1),B(13 ,6),C(13 ,21), and D(3,16)dot If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is (a) (11)/(12) (b) (11)/8 (c) (25)/8 (d) (13)/8

The vertices of a parallelogram A B C D are A(3,1),B(13 ,6),C(13 ,21), and D(3,16)dot If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is (a) (11)/(12) (b) (11)/8 (c) (25)/8 (d) (13)/8