Question

Let \(P\) be the point on the parabola \(y=x^2\) such that the slope of the tangent to the parabola at the point \(P\) is \(4\). Let \(Q\) be the point in the first quadrant lying on the circle \[ x^2+y^2=2 \] such that the slope of the tangent to the circle at the point \(Q\) is \(-1\). Let \(R\) be the point in the first quadrant lying on the ellipse \[ x^2+4y^2=8 \] such that the slope of the tangent to the ellipse at the point \(R\) is \(-\frac12\). Then the radius of the circle passing through the points \(P\), \(Q\) and \(R\) is:

• A. \(\sqrt{10}\)
• B. \(\sqrt5\)
• C. \(\sqrt{\frac52}\)
• D. \(2\sqrt5\)

Hint:

For a right triangle: \[ \mathrm{Circumradius} = \frac{\mathrm{Hypotenuse}}{2} \]

Answer 1

The Correct Option is C