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Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (–2, 0)

Question:

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (–2, 0)

Solution:

Vertex (0, 0) focus (–2, 0)

Since the vertex of the parabola is $(0,0)$ and the focus lies on the negative $x$-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 $(-2,0), a=2$.

Thus, the equation of the parabola is $y^{2}=-4(2) x$, i.e., $y^{2}=-8 x$

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