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(C) Let $P(at^2, 2at)$ be any point on the parabola $y^2 = 4ax$. The equation of the tangent at $P$ is $ty = x + at^2$. It meets the axis $(y=0)$ at $

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$ST = SG = SP$

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(C) Let $P(at^2, 2at)$ be any point on the parabola $y^2 = 4ax$. The equation of the tangent at $P$ is $ty = x + at^2$. It meets the axis $(y=0)$ at $T(-at^2, 0)$.The equation of the normal at $P$ is $y = -tx + 2at + at^3$. It meets the axis $(y=0)$ at $G(2a + at^2, 0)$.The focus $S$ is at $(a, 0)$.$SP = \sqrt{(at^2 - a)^2 + (2at - 0)^2} = \sqrt{a^2(t^2-1)^2 + 4a^2t^2} = \sqrt{a^2(t^4 - 2t^2 + 1 + 4t^2)} = \sqrt{a^2(t^2+1)^2} = a(t^2+1)$.$ST = |x_S - x_T| = |a - (-at^2)| = a(1 + t^2)$.$SG = |x_G - x_S| = |(2a + at^2) - a| = a(1 + t^2)$.Thus,$ST = SG = SP$.

If the tangent and normal at any point $P$ of a parabola meet the axis of the parabola in $T$ and $G$ respectively,then

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