Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$y ^ { 2 } = 24 x$$
A) focus: $( 6,0 )$
directrix: $x = - 6$
B) focus: $( 0,6 )$
directrix: $y = - 6$
C) focus: $( 6,0 )$
directrix: $x = 6$
D) focus: $( 0 , - 6 )$
directrix: $y = - 6$

Question

Quizplus · Accepted Answer

The vertex of the parabola is at the origin, which means that the focus and directrix will both have the same absolute value, but opposite signs. In this case, the coefficient of $x$ is positive, indicating that the parabola opens to the right, and thus the focus will be to the right of the origin. We can use the formula $$4p = 24$$ (where $p$ is the distance from the vertex to the focus/directrix) to solve for the value of $p$, which gives us $p = 6$. Since the focus is to the right of the origin, its coordinates will be $(6,0)$, and since the directrix is a vertical line to the left of the origin, its equation will be $x = -6$.

Graph Parabolas with Vertices at the Origin Find the Focus y2=24xy ^ { 2 } = 24 xy2=24x

Graph Parabolas with Vertices at the Origin
Find the Focus $y ^ { 2 } = 24 x$