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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

hint Hint:

Find the co-ordinates of F ,M and assume the any point N on tangent and Find the length of MN and FN in terms of t to find the ratio in terms of t.

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

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. N is a point on the tangent at P.
F(a,0) and tangent at vertex is x = 0. and P(at²,2at) then foot of perpendicular M is (0,2at)
N is any point on tangent let N = P as Point P also lies on tangent.
Then, MN = at² and
$Error converting from MathML to accessible text.$
Then $Error converting from MathML to accessible text.$

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