If two tangents to the parabola y2 =4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

Question

If two tangents to the parabola y2 =4ax form a point P make angles &theta;1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

Badiuddin askIITians.ismu Expert · Answer

Dear vanya saxena

tangent at parabola at (at₁²,2at₁) is yt₁ =x+at₁²

so tangebt at (at₂²,2at₂) is yt₂ =x+at₂²

these tangent meat at point P

so point p is

{at₁t₂,a(t₁ +t₂)}

also tan Θ₁ =1/t1

tanΘ ₂ =1/t2

and tan(Θ₁ + Θ₂) = tan pi/2

simplify

so t₁t₂ =1

locus of point p

x=at₁t₂

x=a

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sunny redu · Answer

as in the given question the two tangents are perpendicular and the locus of perpendicular tangents is director circle and in case of parabola director circle is directrix and in the question directrix is x=a which is is required locus

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If two tangents to the parabola y2 =4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

If two tangents to the parabola ^y2=4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

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If two tangents to the parabola y2 =4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

If two tangents to the parabola y2=4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2

2 Answers

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If two tangents to the parabola ^y2=4ax form a point P make angles θ1 and theta 2 with the axis of parabola then find the locus of point P such that theta1+theta2=pi/2