Question

The ellipse 4x² + 9y² = 36 and the hyperbola a²x² – y² = 4 intersect at right angles then the equation of the circle through the points of intersection of two conic is

(a) x² + y² = 25

(b) 5(x² + y²) + 3x + 4y = 0

(c) 5(x² + y²) – 3x – 4y = 0

(d) (x² + y²) = 5

Answer 1

Correct option is (d) (x² + y²) = 5

Since ellipse and hyperbola intersect orthogonally, they are confocal.

Let point of intersection in the first quadrant be P(x₁, y₁).

P lies on both the curves.

4x₁² + 9y₁² = 36 and 4x₁² – y₁² = 4

Adding these two, we get

8x₁² + 8y₁² = 40

x₁² + y₁² = 5

Equation of circle is x² + y² = 5.