Question

Write an equation for a parabola in which the set of all points

Answer 1

The equation to use is:

`x=(1)/(4 \left(f - h\right))\left(y-k\right)^2+h`

From the given infor, f=-2, k=0

The equation becomes:

`\begin{gathered} x=(1)/(4(-2-h))(y-0)^2+h \\ x=(1)/(4(-2-h))y^2+h \end{gathered}`

Note that the distance from the focus to vertex is equal to distance from vertex to directrix:

`\begin{gathered} f-h=h-2 \\ -2-h=h-2 \\ -2+2=2h \\ h=0 \end{gathered}`

The equation becomes:

`\begin{gathered} x=(1)/(4(-2-0))y^2+0 \\ x=(1)/(-8)y^2 \\ x=-(1)/(8)y^2 \end{gathered}`

Therefore the required equation is:

`x=-(1)/(8)y^2`