Question

If the tangent to ellipse \(x^2 + 2y^2 = 1\) at point \(P\left(\frac{1}{\sqrt{2}}, \frac{1}{2}\right)\) meets the auxiliary circle at the points \(R\) and \(Q\), then tangents to circle at \(Q\) and \(R\) intersect at

• A. \(\left(\frac{1}{\sqrt{2}}, 1\right)\)
• B. \(\left(1, \frac{1}{\sqrt{2}}\right)\)
• C. \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
• D. \(\left(\frac{1}{2}, \frac{1}{\sqrt{2}}\right)\)

Hint:

Intersection of tangents at ends of chord is pole of the chord.

Answer 1

The Correct Option is A