Find an equation of the parabola described.
-Directrix the line y = 3; vertex at (0, 0)
A) $y = - \frac { 1 } { 12 } x ^ { 2 }$
B) $y = - 12 x ^ { 2 }$
C) $x = 3 y ^ { 2 }$
D) $x = - \frac { 1 } { 12 } y ^ { 2 }$

Question

Find an equation of the parabola described.
-Directrix the line y = 3; vertex at (0, 0) 
A) $y = - \frac { 1 } { 12 } x ^ { 2 }$
B) $y = - 12 x ^ { 2 }$
C) $x = 3 y ^ { 2 }$
D) $x = - \frac { 1 } { 12 } y ^ { 2 }$

Quizplus · Accepted Answer

The directrix is y = 3 and the vertex is at (0, 0), indicating a vertical parabola opening downwards. The distance from the vertex to the directrix is 3 units, so the focus is 3 units in the opposite direction (below the vertex since it opens downwards). The formula for a vertical parabola is $y = a(x - h)^2 + k$, where (h, k) is the vertex. The value of $a$ can be found using the fact that $4a$ is the distance from the vertex to the focus, so $4a = -3$ (negative because the parabola opens downwards), giving $a = -\frac{3}{4}$. However, since the distance is 3, and considering the standard form $y = ax^2$, the correct calculation for $a$ should account for the focus-directrix property, leading to $a = -\frac{1}{4p} = -\frac{1}{12}$, thus the equation is $y = -\frac{1}{12}x^2$.

Find an Equation of the Parabola Described y=−112x2y = - \frac { 1 } { 12 } x ^ { 2 }y=−121​x2

Find an Equation of the Parabola Described $y = - \frac { 1 } { 12 } x ^ { 2 }$