If the length of the semi major axis of an ellipse is 68 and the eccentricity is  then the area of the rectangle formed by joining the vertices of the latera of the ellipse is equal to


Correct option is


Let the equation of the ellipse be  where a2 = (68)2and b2 = (68)2  vertices of the lateral recta are 

Area of the rectangle formed by joining these points


      = 6936.




If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of tangents is


If R is the point of intersection of the tangents to H at the extremities  of the chord L, then equation of the chord contact of with respect to the parabola P is


If the chord of contact of R with respect to the parabola Pmeets the parabola at T and T’, S is the focus of the parabola, then Area of the triangle STT’ is equal to


Tangent are drawn from any point on the hyperbola  to the circle x2 + y2 = 9. If the locus of the mid-point of the chord of contact is



If l is the length of the intercept made by a common tangent to the circle x2 + y= 16 and the ellipse , on the coordinate axes, then 81l2+ 3 is equal to


If d is the length of the tangent from the point (100, 81) to the ellipse , then d2 is equal to


The point of intersection of the perpendicular tangents to the ellipse  lies on a circle square of whose radius is



If x + y = k is a normal to the parabola y2 = 12xp is the length of the perpendicular from the focus of the parabola on this normal; then 3k2 + 2p2 is equal to


If CF is perpendicular from the center C of the ellipse  on the tangent at any point P, and G is the point where the normal at P meets the minor axis, then (CF. PG)2 is equal to


If e1 is the eccentricity of the ellipse  and eis the eccentricity of the hyperbola  and e1e2 = 1, then b2 is equal to