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Let C1 and C2 are circles defined by x...

Let `C_1 and C_2` are circles defined by `x^2+y^2 -20x+64=0` and `x^2+y^2+30x +144=0`. The length of the shortest line segment PQ that is tangent to `C_1` at P and to `C_2` at Q is

A

15

B

18

C

20

D

24

Text Solution

Verified by Experts

The correct Answer is:
C
Centres are (10,0) and (-15 , 0)
`r_(1) = 6 , r_(2) = 9`
d = 25
`r_(1) + r_(2) lt d`
`rArr` Circles are separated
PQ = `lsqrt(d^(2) - (r_(1) + r_(2))^(2)) = sqrt(625 - 225) = 20`
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