Class 11

Math

3D Geometry

Conic Sections

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

Since, the vertex of the parabola is $0,0)$and the focus lies on the negative $x$-axis . So, $x$-axis is the axis of the parabola .

Equation of the parabola is of the form $y_{2}=−4ax$

Since, the focus is $(−2,0)$. So, $a=2$

Thus, the equation of the parabola is $y_{2}=−8x$