Question

write an equation in standard form of an ellipse that is 10 units high and 8 units wide. the center of the ellipse is (0, 0)
options:
\\(\frac{x^2}{25} + \frac{y^2}{16} = 1\\)
\\(\frac{x^2}{64} + \frac{y^2}{100} = 1\\)
\\(\frac{x^2}{16} + \frac{y^2}{25} = 1\\)
\\(\frac{x^2}{100} + \frac{y^2}{64} = 1\\)

Explanation:

Step1: Identify semi-axis lengths

Height (vertical): $10 \implies a = \frac{10}{2}=5$; Width (horizontal): $8 \implies b = \frac{8}{2}=4$

Step2: Apply ellipse standard formula

Center at $(0,0)$, vertical major axis: $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$
Substitute $a=5, b=4$: $\frac{x^2}{4^2} + \frac{y^2}{5^2} = 1 \implies \frac{x^2}{16} + \frac{y^2}{25} = 1$

Answer:

$\frac{x^2}{16} + \frac{y^2}{25} = 1$