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(B) Since the vertex is $(0, 0)$ and the parabola is symmetric about the $y$-axis,the equation of the parabola is of the form $x^{2} = 4ay$.The parabo

Vedclass · Accepted Answer

$2x^{2} = 25y$

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(B) Since the vertex is $(0, 0)$ and the parabola is symmetric about the $y$-axis,the equation of the parabola is of the form $x^{2} = 4ay$.The parabola passes through the point $(5, 2)$.Substituting the point $(5, 2)$ into the equation $x^{2} = 4ay$:$(5)^{2} = 4 	imes a 	imes 2$$25 = 8a$$a = \frac{25}{8}$Substituting the value of $a$ back into the equation:$x^{2} = 4 \left( \frac{25}{8} ight) y$$x^{2} = \frac{25}{2} y$$2x^{2} = 25y$

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(5, 2)$,and symmetric with respect to the $y$-axis.

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