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Find the locus of the point from which t...

Find the locus of the point from which the two tangents drawn to the parabola `y^2=4a x` are such that the slope of one is thrice that of the other.

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The correct Answer is:
`3y^(2)=16ax`
Let the point be (h,k). Let any tangent be
`y=mx+(a)/(m)`
`or" "k=mh+(a)/(m)orm^(2)h-mk+a=0`
Its roots are `m^(1)and3m_(1)`. Therefore,
`m_(1)+3m_(1)=(k)/(h)`
`m_(1)*3m_(1)=(a)/(h)`
Eliminating `m^(1)`, we get the locus as
`3y^(2)=16ax`
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