The number of common tangents to the circles x2+y2=4 and x20+y2-6 x-8 y=24 is

Question

The number of common tangents to the circles x2+y2=4 and x20+y2-6 x-8 y=24 is (A) 0 (B) 1 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

The centres of the given circles x2 + y2 = 4 and x2 + y2 - 6 x - 8 y = 24 are C1 (0, 0) and C2 (3, 4) respectively. Their radii are r1 = 2 and r2 = 7 respectively. C1C2 = 5 < sum of radii But C1C2 = difference of radii Thus, the given circles touch each other internally. Hence, number of common tangent is only one.

Q. The number of common tangents to the circles $x^{2} + y^{2} = 4$ and $x^{20} + y^{2} - 6 x - 8 y = 24$ is

$0$

$1$

$3$

$4$

Q. The number of common tangents to the circles x2+y2=4 and x20+y2−6x−8y=24 is

0

1

3

4

Q. The number of common tangents to the circles $x^{2} + y^{2} = 4$ and $x^{20} + y^{2} - 6 x - 8 y = 24$ is

$0$

$1$

$3$

$4$