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If a tangent to the parabola y^2 = 4ax m...

If a tangent to the parabola `y^2 = 4ax` meets the axis of the parabola in `T` and the tangent at the vertex `A` in `Y,` and the rectangle `TAYG` is completed, show that the locus of `G` is `y^2 + ax = 0.`

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

Equation of tangent to parabola y^(2)=4ax

Knowledge Check

  • A tangent to the parabola y^2=4bx=0 meets the parabola y^2=4ax in P and Q. Then the locus of the middle points of PQ is:

    A
    `x^2(2a+b)=4a^2y`
    B
    `y^2(2a+b)=4a^2x`
    C
    `x^2(2a+b)=2a^2y`
    D
    `y^2(2a+b)=2a^2x`

  • Any tangent to a parabola y^2 = 4ax and perpendicular to it from the focus meet on the line

    A
    ` x=0 `
    B
    `y=0`
    C
    `x=-a`
    D
    `y=-a`

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