Find an equation of the parabola described.
-Focus at (-3, 0); directrix the line x = 3
A) $y ^ { 2 } = - 12 x$
B) $x ^ { 2 } = - 12 y$
C) $y ^ { 2 } = - 3 x$
D) $y ^ { 2 } = 12 x$

Question

Find an equation of the parabola described.
-Focus at (-3, 0); directrix the line x = 3 
A) $y ^ { 2 } = - 12 x$
B) $x ^ { 2 } = - 12 y$
C) $y ^ { 2 } = - 3 x$
D) $y ^ { 2 } = 12 x$

Quizplus · Accepted Answer

The focus of the parabola is at (-3, 0), and the directrix is the vertical line x = 3. This setup indicates a horizontal parabola opening to the left. The distance from the focus to the directrix is 6 units, so the absolute value of 4p (where p is the distance from the vertex to the focus) is 12. Since the parabola opens to the left, the equation takes the form $y^2 = -4px$, which simplifies to $y^2 = -12x$, matching option A.

Find an Equation of the Parabola Described y2=−12xy ^ { 2 } = - 12 xy2=−12x

Find an Equation of the Parabola Described $y ^ { 2 } = - 12 x$