Question

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

• A. $y^{2}=49 x$
• B. $3 y^{2}=-49 x$
• C. $3 y^{2}=49 x$
• D. $x^{2}=-49 y$

Answer 1

Answer: (B)

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) $
$\Rightarrow a=-\frac{49}{12}$.
$\therefore $ The required equation of the parabola is
$y^{2}=4\left(-\frac{49}{12}\right) x \text { or } 3 y^{2}=-49 x$