Question

Find an equation of the ellipse with the following characteristics, assuming the center is at the origin. Major axis horizontal with length 10 ; length of minor axis =6.

Answer 1

The equation of the ellipse is x^2/25 + y^2/9 = 1.

Step-by-step explanation:

To find the equation of the ellipse, we need to use the standard form of the equation for an ellipse:

x^2/a^2 + y^2/b^2 = 1

where a is the semi-major axis and b is the semi-minor axis.

Given that the major axis has a length of 10 and the minor axis has a length of 6, we can determine that the semi-major axis (a) is 5 and the semi-minor axis (b) is 3.

Substituting these values into the equation, we get:

x^2/5^2 + y^2/3^2 = 1

Therefore, the equation of the ellipse is x^2/25 + y^2/9 = 1.