QJEEM18Mace8b: JEE Main 2018 Mathematics - Class 11 JEEM18Mace8b Solution: If a circle C, whose radius is 3, touches externally the…

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

$\therefore$ $\,\,\,$ ${{x - 1} \over 2}$ = 2 $\Rightarrow$ x = 5 and ${{y + 2} \over 2}$ = 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 $\sqrt {{g^2} - c} = 2\sqrt {25 - 20} = 2\sqrt 5$