Mathematics

Problem

A point

P

moves so that the sum of squares of its distances from the points

(1, 2)

and

(-2, 1)

is 14. Let

f(x, y) = 0

be the locus of

P

, which intersects the

x

-axis at the points

A, B

and the

y

-axis at the points

C, D

. Then the area of the quadrilateral

ACBD

is equal to (a)

\frac{9}{2}

(b)

\frac{3\sqrt{17}}{2}

(c)

\frac{3\sqrt{17}}{4}

(d) 9