JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

The locus of the mid-point of the line segment joining the focus of the parabola $y^2=4ax$ to a moving point of the parabola, is another parabola whose directrix is :

x = a

x=-\dfrac a2

x = 0

x=\dfrac a2

Answer and worked solution

Official answer: C

Midpoint of $(a,0)$ and $(at^2,2at)$ : $h=\frac a2(1+t^2)$ , $k=at$ , so $k^2=2a\left(h-\frac a2\right)$ . Vertex $\left(\frac a2,0\right)$ , focal length $\frac a2$ , directrix $x=0$ .

(C)

Topics:Parabola Locus

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 74