The number of common tangents of the circles x2+y2-2x-1=0 and x2+y2-2y-7=0 is

Question

The number of common tangents of the circles x2+y2-2x-1=0 and x2+y2-2y-7=0 is (A)  1  (B)  2  (C)  3  (D)  4

Tardigrade Admin · Accepted Answer

Let S1≡ x2+y2-2x-1=0 Centre, C1=(1, 0) and Radius r1=√1+0+1=√2 and S2=x2+y2-2y-7=0 Centre, C2(0, 1) and Radius r2=√0+1+7=2√2 Here, C1C2=√(1-0)2+(0-1)2=√2 ∵ C1C2=r2-r1 ∴ Circles touch each other internally and so only one common tangent can be drawn to given two circles.

Q. The number of common tangents of the circles $x^{2} + y^{2} - 2 x - 1 = 0$ and $x^{2} + y^{2} - 2 y - 7 = 0$ is

$1$

$2$

$3$

$4$

Q. The number of common tangents of the circles x2+y2−2x−1=0 and x2+y2−2y−7=0 is

1

2

3

4

Q. The number of common tangents of the circles $x^{2} + y^{2} - 2 x - 1 = 0$ and $x^{2} + y^{2} - 2 y - 7 = 0$ is

$1$

$2$

$3$

$4$