Question

If a circle C with center $(5,3)$ touches the circle $x^2+y^2+4x-6y-12=0$ extrenally at a point$(1,-1)$ then the radius of the larger circle C is:

• A. $\sqrt{5}$
• B. $4\sqrt{2}$
• C. $2$
• D. $5$

Answer 1

The correct option is C $2$

$x^2+y^2+4x-6y-12=0$ has centre at $(-2,3)$ and radius $=\sqrt{2^2+3^2+12}=5cm$

Distance between centres of $2$ circles

$=\sqrt{(5-(-2){)}^2+(3-3{)}^2}$

$=7$

$\because$ Circles touch externally.

$\Rightarrow c_1{c}_2=r_1+r_2$

$\Rightarrow 7=5+r$

$\Rightarrow r=2cm$

$\therefore C)$ Answer.