Question

Consider the following equation of a parabola.y2 - 4y = -4x - 8Step of 3: Find the focus of the parabola.

Answer 1

Step-by-step explanation:

Given;

We are given the equation of a parabola as shown below;

`y^2-4y=-4x-8`

Required;

We are required to find the focus of the parabola.

Step-by-step solution;

We re-write this equation and express x in terms of y;

`\begin{gathered} y^2-4y=-4x-8 \\ y^2-4y+8=-4x \\ Multiply\text{ all through by }-1: \end{gathered}`
`\begin{gathered} -y^2+4y-8=4x \\ Divide\text{ all through by 4:} \end{gathered}`
`(4x)/(4)=(1)/(4)(-y^2+4y-8)`
`x=-(1)/(4)(y^2-4y+8)`

We now write this out in the vertex form which is;

`\begin{gathered} x=a(y-b)^2+c \\ Where:vertex=(b,c) \end{gathered}`

We now simplify the right side of the equation;

`x=-(1)/(4)((y-2)^2-4+8)`