Find the expanded form of the ellipse with a center at the origin, a horizontal axis length of 10 and a vertical axis length of 6.
Answer
Substituting these values into the equation of the ellipse, we get the expanded form: \(\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1\)
Step 1 ：Given that the center of the ellipse is at the origin, its equation will be of the form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where a is half of the horizontal axis length and b is half of the vertical axis length.
Step 2 ：We are given that the horizontal axis length is 10, so \(a = \frac{10}{2} = 5\).
Step 3 ：Similarly, the vertical axis length is 6, so \(b = \frac{6}{2} = 3\).
Step 4 ：Substituting these values into the equation of the ellipse, we get the expanded form: \(\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1\)
