The number of common tangents that can be drawn to the circle x2+y2-4 x-6 y-3=0 and x2+y2+2 x+2 y+1=0 is

Question

The number of common tangents that can be drawn to the circle x2+y2-4 x-6 y-3=0 and x2+y2+2 x+2 y+1=0 is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

The two circles are x2+y2-4 x-6 y-3=0 and x2+y2+2 x+2 y+1=0 Center: C 1 ≡(2,3), C 2 ≡(-1,-1) radii: r 1=4, r 2=1 We have C1 C2=5=r1+r2, therefore there are 3 common tangents to the given circles.

Q. The number of common tangents that can be drawn to the circle $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ and $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ is

1

2

3

4

The two circles are $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ and $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$
Center : $C_{1} \equiv (2, 3), C_{2} \equiv (- 1, - 1)$ radii : $r_{1} = 4, r_{2} = 1$
We have $C_{1} C_{2} = 5 = r_{1} + r_{2}$ , therefore there are 3 common tangents to the given circles.

Q. The number of common tangents that can be drawn to the circle x2+y2−4x−6y−3=0 and x2+y2+2x+2y+1=0 is

1

2

3

4

The two circles are x2+y2−4x−6y−3=0 and x2+y2+2x+2y+1=0 Center : C1​≡(2,3),C2​≡(−1,−1) radii : r1​=4,r2​=1 We have C1​C2​=5=r1​+r2​, therefore there are 3 common tangents to the given circles.

Q. The number of common tangents that can be drawn to the circle $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ and $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ is

The two circles are $x^{2} + y^{2} - 4 x - 6 y - 3 = 0$ and $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$
Center : $C_{1} \equiv (2, 3), C_{2} \equiv (- 1, - 1)$ radii : $r_{1} = 4, r_{2} = 1$
We have $C_{1} C_{2} = 5 = r_{1} + r_{2}$ , therefore there are 3 common tangents to the given circles.