Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.
Directrix: $x = - 6$
A) $y ^ { 2 } = 24 x$
B) $y ^ { 2 } = x$
C) $y ^ { 2 } = - 24 x$
D) $x ^ { 2 } = 24 y$
E) $x ^ { 2 } = - 24 y$

Question

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Directrix: $x = - 6$ ​
A) $y ^ { 2 } = 24 x$
B) $y ^ { 2 } = x$
C) $y ^ { 2 } = - 24 x$
D) $x ^ { 2 } = 24 y$
E) $x ^ { 2 } = - 24 y$

Quizplus · Accepted Answer

The directrix of a parabola is perpendicular to the axis of symmetry. Given the directrix $x = -6$, the parabola opens to the right (positive direction along the x-axis) from the vertex at the origin (0,0). The distance from the vertex to the directrix is 6 units, which is the value of $p$ in the parabola's equation $y^2 = 4px$. Substituting $p = 6$ gives $y^2 = 24x$.

Find the Standard Form of the Equation of the Parabola x=−6x = - 6x=−6

Find the Standard Form of the Equation of the Parabola $x = - 6$