Find the equation of the parabola with vertex at (0, 0) and focus at (0, 3).
A) $\quad y ^ { 2 } = 12 x$
B) $\quad x ^ { 2 } = y + 3$
C) $\quad x ^ { 2 } = 3 y$
D) $\quad x ^ { 2 } = 12 y$
E) none of these

Question

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 3). 
A) $\quad y ^ { 2 } = 12 x$
B) $\quad x ^ { 2 } = y + 3$
C) $\quad x ^ { 2 } = 3 y$
D) $\quad x ^ { 2 } = 12 y$
E) none of these

Quizplus · Accepted Answer

A parabola with vertex at (0,0) and focus at (0,3) opens upwards since the focus is above the vertex. The distance from the vertex to the focus is called the focal length and is denoted by 'a'. In this case, a = 3. The equation of the parabola is given by (x - 0)^2 = 4a(y - 0), which simplifies to x^2 = 12y. Therefore, the correct choice is (D).

Find the Equation of the Parabola with Vertex at (0 y2=12x\quad y ^ { 2 } = 12 xy2=12x

Find the Equation of the Parabola with Vertex at (0 $\quad y ^ { 2 } = 12 x$