Yve L. answered • 05/10/23
Experienced High School Math Tutor Specializing in Calculus
The general equation of an ellipse is [(x-h)^2]/a^2 + [(y-k)^2]/b^2 = 1,where
- (h, k) is the center of the ellipse
- 2a is the length of the horizontal axis
- 2b is the length of the vertical axis
The major axis is the axis that is longer.
To find an ellipse equation, you can start with this general form.
In this problem, you start with the following information:
- Ellipse is centered at the origin
- Major axis is horizontal
- Includes the point (3,0)
- Includes the point (0,2)
Let's go through each of those elements.
Centered at the origin: This means (h, k) = (0, 0). Thus, the equation has the form x^2/a^2 + y^2/b^2 = 1. Now you just need to figure out a and b.
Major axis horizontal: This means a > b.
Includes the point (3, 0): This is a point on the x-axis. Because the x-axis passes through the center of the ellipse, you can conclude this is one of the endpoints of the horizontal axis (which is the major axis). Thus, you can say that a = 3.
Includes the point (2, 0): This is a point on the y-axis, which also passes through the center of the ellipse. Thus, you can conclude that this is one of the endpoints of the vertical axis (the minor axis). Thus, you can say b = 2.
Combining this information, you get the ellipse equation x^2/3^2 + y^2/2^2 = 1, equivalently x^2/9 + y^2/4 = 1.