Circumcentre

P(t1) and P(t...

Question

P(t1) and P(t2) are the points t1and t2 on the parabola }y^2=4ax . The normals at }P and }Q meet on } the parabola. Show that the middle point of }PQ lies on the }{ parabola }y^2=2a(x+2a) .

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y^{2} = 4 a x

Δ P Q R

y^{2} = 4 a x

P, Q, R

y^{2} = 4 a x

(h, k)

△ P Q R

P (a t_{1}^{2}, 2 a t_{1})

Q (a t_{2}^{2}, 2 a t_{2})

y^{2} = 4 a x

t_{1} t_{2} = 2

A (t_{1})

B (t_{2})

C (t_{3})

y^{2} = 4 a x,

A B

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