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Find the slopes of the tangents to the p...

Find the slopes of the tangents to the parabola `y^2=8x` which are normal to the circle `x^2+y^2+6x+8y-24=0.`

Text Solution

Verified by Experts

The correct Answer is:
`(2pmsqrt(10))/(3)`
Any tangent to the parabola `y^(2)=8x" is "y=mx+2//m`, which is normal to the given circle.
Hence, the tangents must pass through the centre (-3, -4) of the circle.
Then, we have
`-4=-3m+(2)/(m)`
`or" "3m^(2)-4m-2=0`
`or" "m=(4pmsqrt(40))/(6)=(2pmsqrt(10))/(3)`
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