Find the equation of the parabola with focus | vedclass

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(A) The focus of the parabola is $(2, 0)$,which lies on the $x$-axis. Therefore,the $x$-axis is the axis of the parabola.Since the directrix is $x = -

Vedclass · Accepted Answer

$y^{2} = 8x$

Vedclass · Answer

(A) The focus of the parabola is $(2, 0)$,which lies on the $x$-axis. Therefore,the $x$-axis is the axis of the parabola.Since the directrix is $x = -2$ (which is of the form $x = -a$),the parabola opens to the right and is of the form $y^{2} = 4ax$.Here,the distance from the vertex $(0, 0)$ to the focus $(2, 0)$ is $a = 2$.Substituting $a = 2$ into the standard equation $y^{2} = 4ax$,we get $y^{2} = 4(2)x = 8x$.

Find the equation of the parabola with focus $(2, 0)$ and directrix $x = -2$.

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