Question

If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point :

(1) (√3,0)

(2) (√2,0)

(3) (1, 1)

(4) (–1, 1)

Answer 1

Answer is: (1) (√3,0)

\(\frac{x^2}{4}+\frac{y^2}{1}\) = 1

Equation of tangent is (cosθ)x + 2sinθy = 2

Equation of circle is

so, (√3, 0) satisfying option (1)