JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q28

← JEE Main 2022 · 27 Jun · Shift 1

MathematicsInteger+4 / -1Question 28 of 90

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 ______.

Your answer

Answer and worked solution

Official answer: 16

Centre. On the perpendicular bisector of the side, $y-4=-\frac12(x-2)$ , and on $2x-y+4=0$ : $\left(\frac25,\frac{24}5\right)$ .

Other vertices by reflection through the centre: $(-0.2,7.6)$ and $(-2.2,3.6)$ .

Sides. $\sqrt{20}$ and $\sqrt{(3.2)^2+(1.6)^2}=\sqrt{12.8}$ ; area $\sqrt{256}=16$ .

Answer: 16

Topics:Equation of a circle Distance and section formulae

← Previous question Next question →

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 28