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If perpendiculars are drawn on any tangent to a
parabola $y^{2} = 4 a x$ from the points $(a \pm k, 0)$ on the
axis. The difference of the squares of their lengths
is

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detailed solution

Correct option is D

Any tangent is y=mx+a/m Required differenceis m(a+k)+a/m1+m22−m(a−k)+a/m1+m22=11+m2×4(ma+a/m)mk=4ak

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If perpendiculars are drawn on any tangent to aparabola y2=4axfrom the points (a±k,0) on the axis. The difference of the squares of their lengthsis

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Ready to Test Your Skills?

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If perpendiculars are drawn on any tangent to a
parabola $y^{2} = 4 a x$ from the points $(a \pm k, 0)$ on the
axis. The difference of the squares of their lengths
is