jee-main 2021 Q65

jee-main · India · session3_20jul_shift2 Curve Sketching Sketching a Curve from Analytical Properties

Let $P$ be a variable point on the parabola $y = 4 x ^ { 2 } + 1$. Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y = x$ is:
(1) $( 3 x - y ) ^ { 2 } + ( x - 3 y ) + 2 = 0$
(2) $2 ( 3 x - y ) ^ { 2 } + ( x - 3 y ) + 2 = 0$
(3) $( 3 x - y ) ^ { 2 } + 2 ( x - 3 y ) + 2 = 0$
(4) $2 ( x - 3 y ) ^ { 2 } + ( 3 x - y ) + 2 = 0$

Let $P$ be a variable point on the parabola $y = 4 x ^ { 2 } + 1$. Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y = x$ is:\\
(1) $( 3 x - y ) ^ { 2 } + ( x - 3 y ) + 2 = 0$\\
(2) $2 ( 3 x - y ) ^ { 2 } + ( x - 3 y ) + 2 = 0$\\
(3) $( 3 x - y ) ^ { 2 } + 2 ( x - 3 y ) + 2 = 0$\\
(4) $2 ( x - 3 y ) ^ { 2 } + ( 3 x - y ) + 2 = 0$

Paper Questions

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