Question

match the steps to find the equation of the parabola with Focus (-1, 2), and directrix x=5,find the distance from the focus to the point on the parabola write te equation of the parabolachoose a point on the parabola square both sides and simplifyset the distance from the focus to the point equal to the distance from directrix to the point find the distance from the point on the parabola to the directrix

Answer 1

1. Choose a point on the parabola

`(x,y)`

2. Find the distance from the focus to the point on the parabola.

`\sqrt[]{(x+1)^2+(y-2)^2}`

3. Find the distance from the point on the parabola to the directrix.

`\sqrt[]{(x-5)^2}`

4. Set the distance from the focus to the point equal to the distance from directrix to the point.

`\sqrt[]{(x+1)^2+(y-2)^2}=\sqrt[]{(x-5)^2}`

5. Square both sides and simplify

`\begin{gathered} (x+1)^2+(y-2)^2=(x-5)^2 \\ \end{gathered}`

6. Write the equation of the parabola.

`x=-(y^2)/(12)+(y)/(3)+(5)/(3)_{}`