JEE MAIN - Mathematics (2022 - 27th June Morning Shift - No. 22)
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
16
Explanation
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As slope of line joining (1, 2) and (3, 6) is 2 given diameter is parallel to side
$$\therefore$$ $$a = \sqrt {{{(3 - 1)}^2} + {{(6 - 2)}^2}} = \sqrt {20} $$
and $$b/2 = {4 \over {\sqrt 5 }} \Rightarrow b = {8 \over {\sqrt 5 }}$$
Area $$ = ab = 2\sqrt 5 \,.\,{8 \over {\sqrt 5 }} = 16$$.
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