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find the locus of points of intersection of 2 tangents to parabola which makes an angle A

find the locus of points of intersection of 2 tangents to parabola which makes an angle A

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago

Tangent of coordinate (a.t^2, 2at)

x= a.t^2 y = 2at

 

dx/dt = 2at dy/dt = 2a

dy/dx = dy/dt * dt/dx = 2a/2at = 1/t.

The Equation of Tangent of the Parabola is

y – 2at = (1/t)(x – a.t^2)

à ty – 2.a.t^2 = x – a.t^2

à ty = x + a.t^2

The Point of Intersection of Two Tangents of a Parabola

à t1.y – 2.a..t1^2 = x – a.t1^2

à t2.y – 2.a..t2^2 = x – a.t2^2

Subtracting

à y(t1 – t2) = a(t1^2 – t2^2)

à y = a(t1 + t2)

it follows that x = at1(at1.t2 – a.t^2) = a.t1.t2

I hope, Now you can do it

 

 

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