Question

Find the equation of the parabola with its focus at 6, 2 and it's directrix y = 0

Answer 1

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

`\sqrt[]{(x-6)^2+(y-2)^2}=y-0=y.`

Solving for y we get:

`\begin{gathered} (x-6)^2+(y-2)^2=y^2, \\ (x-6)^2+y^2-4y+4=y^2, \\ (x-6)^2+4=4y, \\ y=(1)/(4)(x-6)^2+1. \end{gathered}`

Answer: First option.