The equation of the parabola with focus (3, 0 | vedclass

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Question

(C) By definition of a parabola,the distance from any point $P(x, y)$ on the parabola to the focus $S(3, 0)$ is equal to the perpendicular distance fr

Vedclass · Accepted Answer

${y^2} = 12x$

Vedclass · Answer

(C) By definition of a parabola,the distance from any point $P(x, y)$ on the parabola to the focus $S(3, 0)$ is equal to the perpendicular distance from $P$ to the directrix $x + 3 = 0$.Let $S = (3, 0)$ and the directrix be $x + 3 = 0$.Using the definition $SP = PM$,where $PM$ is the perpendicular distance to the directrix:$SP^2 = PM^2$$(x - 3)^2 + (y - 0)^2 = (x + 3)^2$$x^2 - 6x + 9 + y^2 = x^2 + 6x + 9$$y^2 = 6x + 6x$$y^2 = 12x$Thus,the correct option is $C$.

The equation of the parabola with focus $(3, 0)$ and the directrix $x + 3 = 0$ is

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