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The number of common tangent(s) to the c...

The number of common tangent(s) to the circles `x^2+y^2+2x+8y-23=0` and `x^2+y^2-4x-10 y-19=0` is 1 (b) 2 (c) 3 (d) 4

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
C
the number ber of …………
`x^(2)+y^(2)+2x+8y-23= 0` ………..(1)
`x^(2)+y^(2)-4x-10y+19 = 0` ………..(2)
`c_(1) -= (-1, -4)` , `r_(1) = sqrt(1+16+23) = 2sqrt(10)`
`c_(2)-= (2, 5)` , `r_(2)= sqrt(4+25-19) = sqrt(10)`
Here `c_(1)c_(2) = sqrt(9+81), r_(1)+r_(2)= 3sqrt(10)`
Hence circles touch each other externally So there are 3 common tangent
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