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

Answer 1

Answer: (B)

$3y^2=-49x$

Axis of the parabola is along the $x-$axis.

So the equation of parabola will be of the form

$(y-k{)}^2=4a(x-h)$

Vertex of parabola is at origin

$\therefore h=0$ and $k=0$

The equation then reduces to

$y^2=4ax$

This parabola passes through the point $(-3,7)$

Substituting this point in the equation of parabola, we get

$(7{)}^2=4a(-3)$

So, $a=-\frac{49}{12}$

Therefore, the equation of parabola is

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

$⟹3y^2=-49x$