MathDB

xy

plane the parabola

K: \ y=\frac{1}{d}x^{2}\ (d: \ positive\ constant\ number)

intersects with the line

y=x

at the point

P

that is different from the origin. Assumed that the circle

C

is touched to

K

P

and

y

axis at the point

Q.

Let

S_{1}

be the area of the region surrounded by the line passing through two points

P,\ Q

and

K,

S_{2}

be the area of the region surrounded by the line which is passing through

P

and parallel to

x

axis and

K.

Find the value of

\frac{S_{1}}{S_{2}}.

Problem Statement