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Maths-

General

Easy

Question

Let F be the focus of the parabola y² = 4ax and M be the foot of perpendicular from point P(at², 2at) on the tangent at the vertex. If N is a point on the tangent at P then $fraction numerator M N over denominator F N end fraction$ equals-

$\frac{t^{2}}{t^{2} + 1}$
$\frac{t^{2} + 1}{t^{2}}$
1
None of these

The correct answer is: $fraction numerator t to the power of 2 end exponent over denominator t to the power of 2 end exponent plus 1 end fraction$

The tangent at any point P on the parabola bisects the angle between the focal chord through P and the line parallel to the axis.
$therefore$ $fraction numerator M N over denominator F N end fraction$ = $fraction numerator a t to the power of 2 end exponent over denominator a t to the power of 2 end exponent plus a end fraction equals fraction numerator t to the power of 2 end exponent over denominator t to the power of 2 end exponent plus 1 end fraction$ .

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