VITEEE 2016 Paper

Let the normal 't1’ cuts the parabola again at the point ‘t2' the equation of the normal
at (at12,2at1) is y + t1x = 2at1+at13
Since it passes through the point 't2' i.e. (at22,2at2)
∴ 2at2+at1t22 = 2at1+at13
⇒ 2a(t1−t2) + at1(t12−t22) =
⇒ 2 + t1(t1+t2) = 0 (Since t1−t2 ≠0)
⇒ 2 + t12+t1t2 = 0
⇒ t1t2 = - (t12+2) ⇒ t2 = - (t1+

2

t1

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