The ellipse `4x^2+9y^2=36` and the hyperbola `a^2x^2-y^2=4` intersect at right angles. Then the equation of the circle through the points of intersection of two conics is `x^2+y^2=5` `sqrt(5)(x^2+y^2)-3x-4y=0` `sqrt(5)(x^2+y^2)+3x+4y=0` `x^2+y^2=25`

Options

A. 1
B. 2
C. 3
D. 4

Answer

B, C, D

Explanation

Since the ellipse and hyperbola intersect orthogonally then they are confocal.
For ellipse `(x^(2))/(9)+(y^(2))/(4)=1`, the foci are `(+-sqrt(5),0)` and for hyperbola `(x^(2))/((4)/(alpha^(2)))-(y^(2))/(4)=1`,
foci are `(+-(2)/(alpha)sqrt(1+alpha^(2)),0)`.
`:. (4)/(alpha^(2))(1+alpha^(2))=5 rArr (4)/(alpha^(2))+4=5rArr alpha^(2)=4rArr alpha=2`.