Solveeit Logo
Login

Question

Question: The circle C has radius 1 and touches the line L at P. The point X lies on C and Y is the foot of th...

The circle C has radius 1 and touches the line L at P. The point X lies on C and Y is the foot of the perpendicular from X to L. The maximum value of the area of PXY as X varies is

A

38\frac{\sqrt{3}}{8}

B

38\frac{3}{8}

C

338\frac{3\sqrt{3}}{8}

D

None of these

Answer

338\frac{3\sqrt{3}}{8}

Explanation

Solution

Let the circle be x2 + (y –1)2 = 1 and the point P be (0,0)

Let X be (cos q, 1 + sin q) Ž area of DPXY

= 12\frac{1}{2} cos q (1 + sin q) = f(q)

Ž f(q) £ 338\frac{3\sqrt{3}}{8}