The number of common tangents to the circles x2+y2=4 and x2+y2-6x-8y-24=0 is

Question

The number of common tangents to the circles x2+y2=4 and x2+y2-6x-8y-24=0 is (A) 4 (B) 3 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

Given, equation of circles are x2 + y2 = 4, whose radius = 2, centre = (0, 0) and x2 + y2 - 6 x - 8 y - 24 = 0, whose radius = √9 + 16- 24 = √1 = 1 and centre = (3 4) Now, c1 c2 = √(3 - 0)2 + (4 - 0)2 = √ 9 + 16 = 5 a1 + a2 = 2 + 1 = 3 Since, c1 c2 > a1 + a2 ∴ Number of common tangents = 4

Q. The number of common tangents to the circles x2+y2=4 and x2+y2−6x−8y−24=0 is

4

3

1

2

Given, equation of circles are x2+y2=4, whose radius = 2, centre = (0, 0) and x2+y2−6x−8y−24=0, whose radius =9+16−24​=1​=1 and centre = (3 4) Now, c1​c2​=(3−0)2+(4−0)2​ =9+16​=5 a1​+a2​=2+1=3 Since, c1​c2​>a1​+a2​ ∴ Number of common tangents = 4

Q. The number of common tangents to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 6 x - 8 y - 24 = 0$ is