Question

The number of common tangents to the circles $x^2+y^2+2x+8y-23=0and{x}^2+y^2-4x-10y+19=0$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C

3

To find the no. of common tangents, let's find the relation between distance between the centers of these circles and sum of their radii -
Co-ordiantes of the center of first circle is (-1, - 4)
Co-ordiantes of the center of second circle is (2, 5)
thus the distance between them is - $\sqrt{(3^2+9^2)}$
= 3$\sqrt{(}10)$
Now, the sum their radii will be -
Radius of the first circle is - 2$\sqrt{(}10)$
Radius of the second circle is - $\sqrt{(}10)$
Sum of them will be - 3$\sqrt{(}10)$
Since, the distance between the centres is equal to sum of their radii
Number of common tangents will be 3.