MathDB

Let

a,\ b

be positive real numbers. Consider the circle

C_1: (x-a)^2+y^2=a^2

and the ellipse

C_2: x^2+\frac{y^2}{b^2}=1.

(1) Find the condition for which

C_1

is inscribed in

C_2

.
(2) Suppose

b=\frac{1}{\sqrt{3}}

and

C_1

is inscribed in

C_2

. Find the coordinate

(p,\ q)

of the point of tangency in the first quadrant for

C_1

and

C_2

.
(3) Under the condition in (1), find the area of the part enclosed by

C_1,\ C_2

for

x\geq p

.
60 point

Problem Statement