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Question

(C) The vertex of the parabola is at $(p, 0)$ on the $x$-axis.The focus is at $(q, 0)$ on the $x$-axis.The distance from the vertex to the focus is $a

Vedclass · Accepted Answer

$y^2 = -4(p - q)(x - p)$

Vedclass · Answer

(C) The vertex of the parabola is at $(p, 0)$ on the $x$-axis.The focus is at $(q, 0)$ on the $x$-axis.The distance from the vertex to the focus is $a = q - p$.The standard equation of a parabola with vertex $(h, k)$ and axis parallel to the $x$-axis is $(y - k)^2 = 4a(x - h)$.Substituting $h = p$,$k = 0$,and $a = q - p$,we get:$(y - 0)^2 = 4(q - p)(x - p)$$y^2 = -4(p - q)(x - p)$.

If the vertex and focus of a parabola lying on the $x$-axis are at distances $p$ and $q$ from the origin respectively,find its equation.

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