Question

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.

Answer 1

The correct answer is 16

Fig.

As slope of line joining (1, 2) and (3, 6) is 2 given diameter is parallel to side
Hence, $a = \sqrt{(3−1)^2+(6−2)^2}$
$= \sqrt{20}$
Thereafter, $\frac{b}{2} = \frac{4}{\sqrt5}$
$⇒ b = \frac{8}{\sqrt5}$
So, the Area ab $= 2 \sqrt5 . \frac{8}{\sqrt5}$
= 16