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)" and " (24,7) are the focii of a hyperbola passing through origin, then

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

Equation of the ellipse with centre at origin, passing through the point (-3,1) and e=sqrt((2)/(5)) is

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

If (3,4) and (5,12) are the foci of two conics both passing through origin, and the eccentricities of the conics are e_(1) and , e_(2) where e_(1)>e_(2) ,then (4e_(1))/(e_(2)) is equal to

If A(1,-1,2),B(2,1,-1)C(3,-1,2) are the vertices of a triangle then the area of triangle ABC is (A) sqrt(12) (B) sqrt(3) (C) sqrt(5) (D) sqrt(13)

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)

A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci at (+-2,0) them the tangent to this hyperbola at P also passes through the point (A)(sqrt(3),sqrt(2))(B)(-sqrt(2),-sqrt(3))(C)(3sqrt(2),2sqrt(3))(D)(2sqrt(2),3sqrt(3))

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) (sqrt(24),5)( B) (sqrt(44),5sqrt(2))( C) (sqrt(44),-5sqrt(2)) (D) (-6,5sqrt(2))