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If the line y=3x+c touches the parabola ...

If the line `y=3x+c` touches the parabola `y^2=12 x` at point `P` , then find the equation of the tangent at point `Q` where `P Q` is a focal chord.

Text Solution

Verified by Experts

The correct Answer is:
`x+3y+27=0`
Line `(1)/(3)y=x+(c)/(3)` touches the parabola `y^(2)=12x`.
Let us compare this line `ty=x+at^(2)orty=x+3t^(2)`.
So, we have `t=(1)/(3)` which is parameter of point P.
Since PQ is focal chord, parameter of point Q is -3.
Therefore, equation of tangent at Q is
`(-3)y=x+3(-3)^(2)`
`or" "x+3y+27=0`
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