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If a tangent to the parabola y^2=4a x me...

If a tangent to the parabola `y^2=4a x` meets the x-axis at `T` and intersects the tangents at vertex `A` at `P ,` and rectangle `T A P Q` is completed, then find the locus of point `Qdot`

Text Solution

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The tangent at point `B(at^(2),2at)` to the parabola is
`ty=x+at^(2)`
Since the tangent at vertex A (0,0) is the y-axis, T and P are `(-at^(2),0)and(0,at)`, respectively.

If Q is (h,k) then `h=-at^(2)` and k=at.
Eliminating t, we get `k^(2)+ah=0`.
Hence, the locus of Q is `y^(2)_ax=0`, which is a parabola.
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