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Circle

The number of...

Question

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

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 $3$
Centre $C_{1} \equiv (2, 3), C_{2} \equiv (- 1, - 1), r_{1} = 4, r_{2} = 1$ .
We have $C_{1} C_{2} = 5 = r_{1} + r_{2}$ .
Hence $3$ common tangents can be drawn.

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