Question

Minimum area of circle which touches the parabola’s y² = x² + 1 and y² = x + 1 is

(a)  9π/32 sq.unit

(b)  π/4 sq.unit

(c)  7π/32 sq.unit

(a)  9π/16 sq.unit

Answer 1

Correct option (a)  9π/32 sq.unit

Explanation:

 y =  x² + 1 and y² = x + 1 are symmetrical about y = x

tangent at point. A and B are parallel to the line y = x

y = x² + 1 

y² = x+1

dy/dx = 2x = 1  y = 1/2

x = 1/2  x = 5/4

y = 5/4

A(1/2,5/4)     B(5/4,1/2)

9π/32 sq.unit