Question

What is the equation of the parabola with focus at (2,4) and directrix y=0?

Answer 1

Okay, here we have this:

Considering the provided information, we are going to find the requested equation of the parabola, so we obtain the following:

According to the information given by substituting in the form of the parabola we have the following equation:

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

Let's solve for y:

`\begin{gathered} y-2=((x-2)^2)/(8) \\ y-2=(x^2-4x+4)/(8) \\ y=(1)/(8)x^2-(1)/(2)x+(1)/(2)+2 \\ y=(1)/(8)x^2-(1)/(2)x+(5)/(2) \end{gathered}`

Finally we obtain that the correct answer is the option D.