# I need to write an equation of an ellipse with these vertices, (see picture). Thanks!?!

Hopefully this helps!

By signing up, you agree to our Terms of Service and Privacy Policy

To write the equation of an ellipse given its vertices, you can use the standard form equation:

[ \frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1 ]

where ((h, k)) represents the coordinates of the center of the ellipse, and (a) and (b) represent the lengths of the semi-major and semi-minor axes, respectively.

Given the vertices ((-3, 0)) and ((3, 0)), the center of the ellipse is the midpoint between these vertices, which is ((0, 0)).

The distance between the center and each vertex represents the length of the semi-major axis, so (a = 3).

Since the ellipse is symmetric across the x-axis, the distance between the center and the co-vertices (the points where the ellipse intersects the y-axis) represents the length of the semi-minor axis, so (b = 3).

Therefore, the equation of the ellipse is:

[ \frac{x^2}{3^2} + \frac{y^2}{3^2} = 1 ]

which simplifies to:

[ \frac{x^2}{9} + \frac{y^2}{9} = 1 ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7