Find the standard form of the parabola with the given characteristic and vertex at the origin.
vertical axis and passes through point $( 10 , - 10 )$
A) $y ^ { 2 } = - 10 x$
B) $x ^ { 2 } = - 10 y$
C) $x ^ { 2 } = \frac { 5 } { 2 } y$
D) $y ^ { 2 } = \frac { 5 } { 2 } x$
E) $y ^ { 2 } = \frac { 5 } { 2 } x ^ { 2 }$

Question

Quizplus · Accepted Answer

The parabola has a vertical axis and passes through (10, -10), indicating it opens downwards. The standard form for a vertical parabola is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Substituting the point (10, -10) into $x^2 = 4py$ gives $10^2 = 4p(-10)$, solving for $p$ gives $p = -\frac{10}{4} = -\frac{5}{2}$, so the equation becomes $x^2 = -10y$.

Find the Standard Form of the Parabola with the Given (10,−10)( 10 , - 10 )(10,−10)

Find the Standard Form of the Parabola with the Given $( 10 , - 10 )$