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The tangents to the parabola `y^2=4a x`at the vertex `V`and any point `P`meet at `Q`. If `S`is the focus, then prove that `S PdotS Q ,`and `S V`are in GP.A. `A.P.`B. `G.P.`C. `H.P.`D. none of these |
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Answer» Correct Answer - B Let `y^(2)=4ax` be a parabola with vertex at A(0, 0) and `P(at^(2), 2at)` be any point on it. The equation of tangents at A and P are x=0 and `ty=x+at^(3)` respectively. These two intersect at Q(0, at). The focus S of dsthe parabola `y^(2)=4ax` has coordinates (a, 0). `:." "SP=a+at^(2),SQ=ssqrt(1+t^(2))" and "SA=a` ltrbgt `rArr" "SQ^(2)=SPxxSArArrSP, SQ, SA" are in G.P."` |
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