Through the vertex 'O' of the parabola y 2 = 4ax, variable chords OP and OQ are drawn at right angles. If the variable chord PQ intersects the axis of x at R, then the distance OR is equal to
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Let the equation of line PQ be y = mx + c
by homogenization
y 2 = 4ax 
⇒ y 2 + 
– 
= 0
It is the equation of ⊥ r lines passing through 0(0, 0), then coefficient of x 2 + coefficient of y 2 = 0
Hence 1 + 
= 0 ⇒ 
= – 
.........(1)
y = mx + c cuts the x-axis
at R 
⇒ OR = – 
= 4a [from (i)]
Hence OR = 4a = Latus Rectum
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