If a circle C passing through (4, 0) touches the circle x2 + y2 + 4x - 6y - 12 = 0 externally at a point (1, -1), then the radius of the circle C is :

Question

If a circle C passing through (4, 0) touches the circle x2 + y2 + 4x - 6y - 12 = 0 externally at a point (1, -1), then the radius of the circle C is : (A) 5 (B) 2√5 (C) 4 (D) √57

Tardigrade Admin · Accepted Answer

Let A be the centre of given circle and B be the centre of circle C. x2+y2+4x-6y-12=0 ∴ A=(-2, 3) and B=(g. f) Now, from the figure, we have (-2+g/2)=1 and (3+f/2)=-1 (By mid point formula) ⇒ g=4 and f= - 5 Now, required radius =OB=√9+16=√25=5

Q. If a circle $C$ passing through $(4, 0)$ touches the circle $x^{2} + y 2 + 4 x - 6 y - 12 = 0$ externally at a point $(1, - 1)$ , then the radius of the circle $C$ is :

$5$

$25$

$4$

$57$

Q. If a circle C passing through (4,0) touches the circle x2+y2+4x−6y−12=0 externally at a point (1,−1), then the radius of the circle C is :

5

25​

4

57​

Let A be the centre of given circle and B be the centre of circle C. x2+y2+4x−6y−12=0 ∴A=(−2,3​) and B=(g.f) Now, from the figure, we have 2−2+g​=1 and 23+f​=−1 (By mid point formula) ⇒g=4 and f=−5 Now, required radius =OB=9+16​=25​=5

Q. If a circle $C$ passing through $(4, 0)$ touches the circle $x^{2} + y 2 + 4 x - 6 y - 12 = 0$ externally at a point $(1, - 1)$ , then the radius of the circle $C$ is :

$5$

$25$

$4$

$57$