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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).

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).

Grade:12th pass

2 Answers

Arun
25763 Points
one year 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
14149 Points
one year ago
Dear student 
For more details and examples Please follow this link 
Good Luck 

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