Question

How do you find the coordinates of the center, foci, the length of the major and minor axis given `36x^2+81y^2=2916`?

Answer 1

You can obtain your answers by doing steps 1 through 4 in the explanation.

Explanation:

Let divide by 2916 and write the denominators as squares:

`x^2/9^2 + y^2/6^2 = 1`

When the denominator of the x term is greater than the denominator of the y term, the standard form is:

`(x - h)^2/a^2 + (y - k)^2/b^2 = 1`

where:

1. `(h, k)` is the center point
2. `2a` is the length of the major axis
3. `2b` is the length of the minor axis
4. The foci are at `(h + sqrt(a^2 - b^2), k)` and `(h - sqrt(a^2 - b^2), k)`

Subtract zero from x and y to put the equation in standard form:

`(x - 0)^2/9^2 + (y - 0)^2/6^2 = 1`

You can do steps 1 through 4 for your answer.