# Find the equation of the parabola that satisfies the following conditions:

Question:

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

Solution:

Vertex (0, 0); focus (3, 0)

Since the vertex of the parabola is $(0,0)$ and the focus lies on the positive $x$-axis, $x$-axis is the axis of the parabola, while the equation of the parabola is of the form $y^{2}=4 a x$.

Since the focus is (3, 0)a = 3.

Thus, the equation of the parabola is $y^{2}=4 \times 3 \times x$, i.e., $y^{2}=12 x$