JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q82

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MathematicsSingle correct+4 / -1Question 82 of 90

Let O be the vertex and Q be any point on the parabola, $x^2=8y$ . If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

x^2=y

y^2=x

y^2=2x

x^2=2y

Answer and worked solution

Official answer: D

$Q=(4t,2t^2)$ and $P=\frac14Q=\left(t,\frac{t^2}2\right)$ , so the locus is $x^2=2y$ .

Topics:Parabola Locus

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JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 82