The equation of the parabola with the focus ( | vedclass

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(C) Given that the focus is $S(3,0)$ and the directrix is $x+3=0$. Let $P(x, y)$ be any point on the parabola.By the definition of a parabola,the dist

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$y^2=12x$

Vedclass · Answer

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

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

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