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 ________.
Correct Answer: 16
Solution and Explanation
The correct answer is 16
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
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