NIMCET 2023 Question Paper with solutions

Question : 50 of 120

Marks: +1, -0

The locus of the mid points of all chords of the parabola

y^2=4 x

, which are drawn through its vertex, is:

Solution:

Let mid point of VP is

{M}(h, k)

h\;=\;{0+a t^2}/{2}

⇒ \;\; a t^2\;=2 h

......(i)

k\;=\;{0+2 a t}/{2}

⇒ \;\; a t\;=k ⇒ t=\;{k}/{a}

Put value of

t

in equation (i) we get

k^2=2 a h

Replace

h \to x

and

k \to y

y^2=2 a x

By given parabola,

y^2\;=4 x

a\;=1

Hence, locus of the mid-point of all chord is

y^2=2 x

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