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show that the tangents to the parabola y^2=4ax at the ends f the latus rectum meet at its directrix

show that the tangents to the parabola y^2=4ax at the ends f the latus rectum meet at its directrix

Grade:11

1 Answers

sahil
142 Points
6 years ago
Sol:take the parabola as y^2=4ax now cordinates of its end of latus rectum are (a,2a) ; (a,-2a).Now tangent at any point (x`,y`) on parabola is yy`=2a(x+x`).Tangent at point (a,2a) is 2ay=2ax+2a^2 and at (a,-2a) is -2ay=2ax+2a^2 .Solve this linear equation in two unknown to get point of intersection of tangent y=0 and x=-a ;so the point of intersection is (-a,0) and it clearly lie on directrix. If it was helpful pleaseapprove my answer.

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