The equation of the parabola whose vertex and | vedclass

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(A) The standard form of a parabola with vertex at $(h, k)$ and axis parallel to the $x$-axis is $(y - k)^2 = 4A(x - h)$.Given the vertex is at $(a, 0

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$y^2 = 4(a' - a)(x - a)$

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(A) The standard form of a parabola with vertex at $(h, k)$ and axis parallel to the $x$-axis is $(y - k)^2 = 4A(x - h)$.Given the vertex is at $(a, 0)$,we have $h = a$ and $k = 0$.Thus,the equation is $y^2 = 4A(x - a)$.The focus is at $(a', 0)$. For a parabola $y^2 = 4A(x - h)$,the focus is at $(h + A, k)$.Therefore,$a + A = a'$,which gives $A = a' - a$.Substituting $A$ into the equation,we get $y^2 = 4(a' - a)(x - a)$.

The equation of the parabola whose vertex and focus lie on the $x$-axis at distances $a$ and $a'$ from the origin,respectively,is

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