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Question

If two normals to a parabola y2=4ax intersect at right angles, then the chord joining their feet passes through a fixed point whose coordinates are

A
(2a,0)
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B
(a,0)
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C
(2a,0)
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D
(a,0)
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Solution

The correct option is B (a,0)
Given parabola is y2=4ax
Let P(at21,2at1) and Q(at22,2at2) be two points on the parabola.
Slope of normal at P is m1=t1
Slope of normal at Q is m2=t2
normals are perpendicular to each other,
m1m2=1t1t2=1
which is the required condition for focal chord.
So, chord passes through the fixed point (a,0)

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