A model of the form $y ^ { 2 } = 4 p x$ is given. Identify the focus, and write an equation for the directrix.
-$$y ^ { 2 } = - 3 x$$
A) focus: $\left( - \frac { 3 } { 4 } , 0 \right)$; directrix: $x = \frac { 3 } { 4 }$
B) focus: $\left( 0 , \frac { 3 } { 4 } \right)$; directrix: $y = - \frac { 3 } { 4 }$
C) focus: $\left( - \frac { 3 } { 4 } , 0 \right) ;$ directrix: $x = - \frac { 3 } { 4 }$
D) focus: $\left( 0 , - \frac { 3 } { 4 } \right) ;$ directrix: $y = \frac { 3 } { 4 }$

Question

Quizplus · Accepted Answer

The given equation $y^2 = -3x$ is a parabola that opens to the left. The standard form is $y^2 = 4px$, so $4p = -3$, giving $p = -\frac{3}{4}$. The focus is $(-p, 0) = \left(-\frac{3}{4}, 0\right)$ and the directrix is $x = p = \frac{3}{4}$.

A Model of the Form y2=4pxy ^ { 2 } = 4 p xy2=4px

A Model of the Form $y ^ { 2 } = 4 p x$