Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.
Horizontal axis and passes through the point $( - 4,7 )$
A) $x ^ { 2 } = \frac { - 4 } { 49 } y$
B) $y ^ { 2 } = \frac { - 4 } { 49 } x$
C) $y ^ { 2 } = \frac { 49 } { - 4 } x$
D) $x ^ { 2 } = \frac { 49 } { - 4 } y$
E) $y ^ { 2 } = x$

Question

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Horizontal axis and passes through the point $( - 4,7 )$ ​
A) $x ^ { 2 } = \frac { - 4 } { 49 } y$
B) $y ^ { 2 } = \frac { - 4 } { 49 } x$
C) $y ^ { 2 } = \frac { 49 } { - 4 } x$
D) $x ^ { 2 } = \frac { 49 } { - 4 } y$
E) $y ^ { 2 } = x$

Quizplus · Accepted Answer

Since the parabola has a horizontal axis and passes through the point $(-4,7)$, its equation must be in the form $y^2 = 4px$, where $p$ is the distance from the vertex to the focus. Substituting $(-4,7)$ into $y^2 = 4px$ gives $7^2 = 4p(-4)$, solving for $p$ gives $p = \frac{49}{-4}$, thus the correct equation is $y^2 = \frac{49}{-4}x$.

Find the Standard Form of the Equation of the Parabola (−4,7)( - 4,7 )(−4,7)

Find the Standard Form of the Equation of the Parabola $( - 4,7 )$