If the ellipse 4 x^2+9 y^2=36 is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hyperbola lie on the circle

Step-by-step solution

Ellipse : 4 x^2+9 y^2=36 ....(i) and Hyperbola = x^2 1 - y^2 b^2 =1 b^2 x^2-y^2=b^2 As, they are confocal (a e)^2=a^2+b^2 5=1+b^2 b^2=4 So, hyperbola 4 x^2-y^2=4 .....(ii) Adding (i) and (ii), 8 x^2+8 y^2=40 x^2+y^2=5 intersection lies on this circle.