JEE Main 2018 — Circle Question with Solution

Given circle is :

x² + y² + 2x $$-$$ 4y $$-$$4 = 0

$$\therefore$$ its center is ($$-$$ 1, 2) and radius is 3 units.

Let A = (x, y) be the center of the circle C

$$\therefore$$ $$\frac{x-1}{2}$$ = 2 $$\Rightarrow$$ x = 5 and $$\frac{y+2}{2}$$ = 2 $$\Rightarrow$$ y = 2

So the center of C is (5, 2) and its radius is 3

$$\therefore$$ Equation of center C is :

x² + y² $$-$$ 10x $$-$$ 4y + 20 = 0

$$\therefore$$ The length of the intercept it cuts on the x-axis

= 2$$\sqrt{g^2-c}=2\sqrt{25-20}=2\sqrt{5}$$