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Find the number of common tangent to the...

Find the number of common tangent to the circles `x^2+y^2+2x+8y-23=0` and `x^2+y^2-4x-10 y+9=0`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
3
`C_(1)-=(-1,-4),C_(2) -=(2,5)`
`r_(1)=sqrt(1+16+23)=2sqrt(10)`
`r_(2)=sqrt(4+25-19)=sqrt(10)`
`C_(1)C_(2)=sqrt(9+81)=3sqrt(10)`
`:. C_(1)C_(2)=r_(1)+r_(2)`
Hence, the circle touch externally.
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