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Prove that the length of the intercept o...

Prove that the length of the intercept on the normal at the point `P(a t^2,2a t)` of the parabola `y^2=4a x` made by the circle described on the line joining the focus and `P` as diameter is `asqrt(1+t^2)` .

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Knowledge Check

  • If the normals at points 't_1' and 't_2' meet on the parabola, then

    A
    `t_1t_2=-1`
    B
    `t_2 =-t_1 -2/t_1`
    C
    `t_1t_2=2`
    D
    none of these

  • The normal at the point P( "at"_1^2,2at_1) meets the parabola y^2 = 4ax again at Q (at_2^2, 2at_2) such that the lines joining the origin to P and Q are at right angle, then

    A
    `t_1^2 = 2 `
    B
    `t_2^2 = 2`
    C
    `t_1 = 2t_2`
    D
    `t_2 = 2t_1`

  • If the normals drawn at the points t_(1) & t_(2) on the parabola y^(2)=4ax meet the parabola again at its point t_(3) , then t_(1)t_(2) equals:

    A
    2
    B
    `-1`
    C
    `-2`
    D
    `t_(3)-(2)/(t_(3))`