Question

Tony is trying to find the equation of a quadratic that has a focus of (-1, 4) and a directrix of y = 8. Describe to Tony your preferred method for deriving the equation. Make sure you use Tony's situation as a model to help him understand. (10 points)

Answer 1

Personally, given the Focus and Directrix, I prefer the DEFINITION.

All points (x,y) such that.

Distance from Focus: \(\sqrt{(x+1)^{2}+(y-4)^{2}}\)
Distance from Directrix: \(y-8\)
Are equal: \(\sqrt{(x+1)^{2}+(y-4)^{2}} = y-8\)

A little algebra later...

\((x+1)^{2}+(y-4)^{2} = (y-8)^{2}\)
\((x+1)^{2}+(y^{2} - 8y + 16) = (y^{2}-16y + 64)\)
\((x+1)^{2}+( - 8y + 16) = ( -16y + 64)\)
\((x+1)^{2}+(16) = ( -8y + 64)\)
\((x+1)^{2} = ( -8y + 48)\)
\((x+1)^{2} = -8(y - 6)\)

Vertex: (-1,6)
Distance to Focus: 2
Distance to Directrix: 2

I think we have it.

Answer 2

can you summarize that into a paragraph that's worth 10ish points?

Answer 3

Already did. Most of what you see is the algebra. It is just the DEFINITION. It is not anything more.

Answer 4

so I just type in all the math and say the distances and that's it?

Answer 5

" Describe to Tony your preferred method for deriving the equation."

Is that YOUR method? I showed you how to use the definition. If you "just type in all that math", then I'm afraid you do not understand this methodology and it cannot be construed as "your preferred method".

What is your preferred method? This is the question. If it is your preferred method, you should be able to apply it and describe it and understand it.

Answer 6

okie.