Question

Find the equation of the ellipse with the given properties: Vertices at (±36,0) and (0,±25) =1

Answer 1

The equation of the ellipse with the given properties is x²/36² + y²/25² = 1.

Step-by-step explanation:

To find the equation of the ellipse, we can use the standard form of the ellipse equation:

(x-h)²/a² + (y-k)²/b² = 1

Where (h, k) is the center of the ellipse, and 'a' and 'b' are the lengths of the semi-major axis and semi-minor axis, respectively.

In this case, the center of the ellipse is (0, 0), and the lengths of the semi-major and semi-minor axis are 36 and 25, respectively. So, the equation of the ellipse is:

x²/36² + y²/25² = 1

Answer 2

The equation of the ellipse is
`x^2/1296 + y^2/625 = 1`

Step-by-step explanation:

The equation of an ellipse with vertices at (±36,0) and (0,±25) can be found using the formula:

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

where (h, k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis.

In this case, the center of the ellipse is (0,0), the semi-major axis is 36, and the semi-minor axis is 25.

Plugging these values into the formula, we get:

`x^2/1296 + y^2/625 = 1`