Question

guided practice
type your answer and then click or tap done.
write the equation for an ellipse with foci (±2, 0) and co - vertices (0, ±4).
\\(\frac{x^2}{\square}+\frac{y^2}{\square}=1\\)

Explanation:

Step1: Identify given values

Foci $(\pm 2, 0)$ so $c=2$; co-vertices $(0, \pm 4)$ so $b=4$

Step2: Calculate $a^2$

Use $c^2 = a^2 - b^2$, so $a^2 = c^2 + b^2 = 2^2 + 4^2 = 4 + 16 = 20$

Step3: Write ellipse equation

Substitute $a^2=20$, $b^2=16$ into $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$: $\frac{x^2}{20} + \frac{y^2}{16} = 1$

Answer:

$\frac{x^2}{20} + \frac{y^2}{16} = 1$