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Question

The number of common tangents to the circles x2+y2+2x+8y−23=0 and x2+y2−4x−10y+19=0 is


A

1

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B

2

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C

3

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D

4

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Solution

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 - (32+92)
= 3(10)
Now, the sum their radii will be -
Radius of the first circle is - 2(10)
Radius of the second circle is - (10)
Sum of them will be - 3(10)
Since, the distance between the centres is equal to sum of their radii
Number of common tangents will be 3.


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