Question by BLACKPEOPLE: How do i determine the domain and range for a ellipse?
How do i determine the domain and range for a ellipse?

Is there a website where i can drop a figure and it will show me the equation, range and the domain?

I am working on the following project:

“students design an appropriate logo for a company. They use a combination of conics (and other functions) to create their logo designs. Students must write equations, domains, and ranges that will reproduce the designs”

I’m not sure that “domain” and “range” properly apply to something that is not a function — which an ellipse is not, because it fails the “vertical line test” — but if the ellipse is written in standard form:

(x – h)²/a² + (y – k)²/b² = 1

Then the “domain” (in the sense of the x-values for which there will be at least one corresponding y-value) would be:

[h – a, h + a]

And the domain would be:

[k – b, k + b]

so for example:

(x – 3)²/9 + (y – 7)²/25 = 1

would have “domain” [3 – 3, 3 + 3] or [0, 6], and range [7 – 5, 7 + 5], or [2, 12].