Let $P$be the parabola, whose focus is $(-2,1)$ and directrix is $2x+y+2=0$. Then the sum of the ordinates of the points on $P$, whose abscissa is $-2$ , is [JEE Main 2025, 7 Apr (Shift 1)]

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YESPYQ · Accepted Answer

Correct answer: a) $\frac{3}{2}$. Let point $P(-2,y)$ is point on parabola from def. of parabola $PS=PM$ $\Rightarrow {(y−1)}^{2}=\frac{{(−4+y+2)}^{2}}{5}$ $\Rightarrow 5{(y−1)}^{2}={(y−2)}^{2}$ $\Rightarrow 4{y}^{2}−6y+1=0$ Sum of roots $=\frac{6}{4}=\frac{3}{2}$

Let \(P\)be the parabola, whose focus is \((-2,1)\) and directrix is \(2x+y+2=0\). Then the sum of the ordinates of the …

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