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The equation of the parabola with vertex at origin, which passes through the point $(- 3, 7)$ and axis along the x-axis is

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$y^{2} = 49 x$

$3 y^{2} = - 49 x$

$3 y^{2} = 49 x$

$x^{2} = - 49 y$

answer is B.

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Detailed Solution

Let a parabola with vertex at origin and axis along the x-axis be $y^{2} = 4 a x$ . It passes through $(- 3, 7)$

hence $(7)^{2} = 4 a (- 3) \Rightarrow a = - \frac{49}{12} .$

$∴$ The required equation of the parabola is

$y^{2} = 4 (- \frac{49}{12}) x or 3 y^{2} = - 49 x$

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