JEE Main 2019 — Circle Question with Solution

Distance beetween point A and B is = 14 unit

As y coordinate of point A(-8, 5) and B(6, 5) are same. So line AB is parallel to the x axis.

Point O is the center of the circle and OP is the perpendicular to the line AB. And P is the mis point of line AB.

$$\therefore$$ Point P = $$\left(\frac{-8+6}{2},\frac{5+5}{2}\right)$$ = (-1, 5)

As OP is perpendicular to the line AB and AB is parallel to the x axis then OP is parallel to the y axis. So x coordinate of line OP is constant.

$$\therefore$$ x coordinate of O = -1

And point O is lies on the line 3y = x + 7

$$\therefore$$ 3y = -1 + 7

$$\Rightarrow$$ y = 2

$$\therefore$$ Center O = (-1, 2)

$$\therefore$$ OP = 3

Then BC = 2OP = 6

$$\therefore$$ Area of rectangle = (AB)(BC)

= 14 $$\times$$ 6

= 84