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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

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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. `2sqrt(5)`
C. 5
D. `3sqrt(5)`
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Correct Answer - C
The line `5x-2y+6=0` cuts y-axis y at Q(0, 3).
Clearly, PQ is the length of the tangent drawn from Q on the circle `x^(2)+y^(2)+6x+6y-2=0`.
`:.PQ=sqrt(0+9+6xx0+6xx3-2)=5`
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