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If the tangent at the point on the circl...

If the tangent at the point on the circle `x^2+y^2+6x +6y=2` meets the straight ine `5x -2y+6 =0` at a point Q on the y- axis then the length of PQ is

A

4

B

`2sqrt5`

C

5

D

`3sqrt5`

Text Solution

Verified by Experts

The correct Answer is:
C
The line 5x - 2y + 6 = 0 meets the Y-axis at the point (0,3) and therefore the tangent has to pass through the point (0,3) and required length
`=sqrt(x_(1)^(2)+y_(1)^(2)+6x_(1)+6y_(1 )-2)`
`=sqrt((0^(2)+3^(2)+6(0)+6(3)-2))`
`=sqrt25=5`
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