Analytical Geometry> If the normals to the parabola y^2 = 4ax ...

If the normals to the parabola y^2 = 4ax at the points t1 & t2 intersect again on the parabola at the point ‘t3’ then t1*t2 = 2 ; t3 = – (t1 + t2) and hence prove that the line joining t1 & t2 passes through a fixed point (–2a, 0).

Praveen Kumar Das , 5 Years ago

Grade 12th pass

2 Answers

Arun

Last Activity: 5 Years ago

Dear student

normal to Equation at ‘t'

y = – t x + 2at + at^3

t^3 + t(2a-x) – y = 0

as it has three roots t1, t2, t3

hence t1 + t2 + t3 = 0

hence t3 = – (t1 + t2)

Vikas TU

Last Activity: 5 Years ago

Dear student

For more details and examples Please follow this link

https://www.askiitians.com/iit-jee-coordinate-geometry/normal-to-a-parabola.aspx

Good Luck

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Analytical Geometry> If the normals to the parabola y^2 = 4ax ...

If the normals to the parabola y^2 = 4ax at the points t1 & t2 intersect again on the parabola at the point ‘t3’ then t1*t2 = 2 ; t3 = – (t1 + t2) and hence prove that the line joining t1 & t2 passes through a fixed point (–2a, 0).

Praveen Kumar Das , 5 Years ago

Arun

Vikas TU

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