Equation of the parabola whose vertex is $(0, 0)$ and focus is the point of intersection of the lines $x + y = 2, 2 x - y = 4$ is

y^{2} = 2 x

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y^{2} = 4 x

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y^{2} = 8 x

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x^{2} = 8 y

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Solution

The correct option is D $y^{2} = 8 x$
$(y - 0)^{2} = 4 a (x - 0)$
$x + y = 2$
$2 x - y = 4$
$\Rightarrow x = 2, y = 0$
Focus is $(a, 0) = (2, 0)$
$y^{2} = 8 x$

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Equation of the parabola whose vertex is (0,0) and focus is the point of intersection of the lines x+y=2,2x−y=4 is

The correct option is D y2=8x(y−0)2=4a(x−0)x+y=22x−y=4⇒x=2,y=0Focus is (a,0)=(2,0)y2=8x

Equation of the parabola whose vertex is $(0, 0)$ and focus is the point of intersection of the lines $x + y = 2, 2 x - y = 4$ is

The correct option is D $y^{2} = 8 x$
$(y - 0)^{2} = 4 a (x - 0)$
$x + y = 2$
$2 x - y = 4$
$\Rightarrow x = 2, y = 0$
Focus is $(a, 0) = (2, 0)$
$y^{2} = 8 x$