If p be the perpendicular distance of a focal chord PQ of length l from the vertex A of the parabola y2=4ax, then l varies inversely as
A
p2
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B
1p2
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C
p
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D
1p
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Solution
The correct option is B1p2 ∵PQ is focal chord ∴l=a(t+1t)2 Also chord equation joining points t1,t2 is y(t1+t2)−2x−2at1t2=0 ∵PQ is focal chord y(t−1t)−2x+2a=0 p=2a√(t−1t)2+4 ∴p2=4a2(t+1t)2 Clearly, lp2=4a3(constant)