Since chords are perpendicular, therefore if one makes an angle θ then the other will make an angle (90° – θ ) with x-axis

Let AP = r 1 and AQ = r 2

If ∠ PAX = θ

then ∠ QAX = 90° – θ

∴ Coordinates of P and Q are (r 1 cos θ , r 1 sin θ ) and (r 2 sin θ , r 2 cos θ ) respectively

Since P and Q lies on y 2 = 4ax

∴ sin 2 θ = 4ar 1 cos θ and cos 2 θ = 4ar 2 sin θ

⇒ r 1 = and r 2 =

∴ (r 1 r 2 ) 4/3 = ...(i)

and 16a 2 = 16a 2

= 16a 2 .(4a) 2/3

= 16a 2 .(4a) 2/3

=

= (r 1 r 2 ) 4/3 [from (i)]

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