If a tangent to the ellipse x 2 + 4 y 2 = 4 meets the tangents at the extremities of its major axis at B and C , then the circle with B C as diameter passes through the point.

Step-by-step solution

We have, x 2 4 + y 2 1 = 1 Equation of tangent is cos θ x + 2 sin θ y = 2 B - 2 , 1 + cos θ sin θ , C 2 , 1 - cos θ sin θ ≡ B - 2 , cot θ 2 , C 2 , tan θ 2 Equation of required circle will be x + 2 x - 2 + y - cot θ 2 y - tan θ 2 = 0 ⇒ x 2 - 4 + y 2 - tan θ 2 + cot θ 2 y + 1 = 0 Hence, 3 , 0 satisfies the above equation.