If the tangents at P and Q on a parabola meet | vedclass

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(B) Let $P(at_1^2, 2at_1)$ and $Q(at_2^2, 2at_2)$ be two points on the parabola $y^2 = 4ax$. Then the tangents at $P$ and $Q$ intersect at $T(at_1t_2,

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$G.P.$

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(B) Let $P(at_1^2, 2at_1)$ and $Q(at_2^2, 2at_2)$ be two points on the parabola $y^2 = 4ax$. Then the tangents at $P$ and $Q$ intersect at $T(at_1t_2, a(t_1 + t_2))$. Now,$SP = \sqrt{(at_1^2 - a)^2 + (2at_1 - 0)^2} = a(t_1^2 + 1)$. $SQ = a(t_2^2 + 1)$. $ST = \sqrt{(at_1t_2 - a)^2 + (a(t_1 + t_2) - 0)^2} = a\sqrt{(1 + t_1^2)(1 + t_2^2)}$. Therefore,$ST^2 = a^2(1 + t_1^2)(1 + t_2^2) = SP \cdot SQ$. Since $ST^2 = SP \cdot SQ$,the terms $SP, ST, SQ$ are in $G.P.$

If the tangents at $P$ and $Q$ on a parabola meet at $T$,then $SP, ST$ and $SQ$ are in

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