If two perpendicular tangents can be drawn from the origin to the circle `x^2-6x+y^2-2p y+17=0` , then the value of `|p|` is___

Answer

5

Explanation

The equation of the given circle is
`x^(2)+y^(2)-6x-2py+17=0`
or `(x-3)^(2)+(u-p)^(2)=(p^(2)-8)` (1)
Also, `(0,0)` lies outside the circle.
The equation of director circle of `S=0` will be
`(x-3)^(2)+(u-p)^(2)=2(p^(2)-8)` (2)
Tangents drawn from `(0,0)` to circle (1) are perpendicular to each other.
Therefore, `(0,0)` must lie on director circle. Hence,
`(0-3)^(2)+(0-p)^(2)=2(p^(2)-8)`
or `p^(2)=25`
or `p= +-5`