Question

Find the equation of the parabola with its focus at -5,0 and it's directrix y = 2

Answer 1

Recall that a parabola is a curve where any point is at an equal distance from the focus and the directrix, if (x,y) is a point on the parabola then:

`\sqrt[]{(-5-x)^2+(y-0)^2}=2-y\text{.}`

Solving for y we get:

`\begin{gathered} (-5-x)^2+y^2=(2-y)^2, \\ (x+5)^2+y^2=4-4y+y^2, \\ -4y=(x+5)^2-4, \\ y=-(1)/(4)(x+5)^2+(4)/(4), \\ y=-(1)/(4)(x+5)^2+1. \end{gathered}`

Answer: Second option.