Question

convert the following equation for an ellipse to standard form.

9x² + 36y² + 90x + 288y + 477 = 0

standard form

graph the ellipse.

Explanation:

Step1: Group \(x\) and \(y\) terms

$$
LATEXBLOCK0
$$

Step2: Factor out coefficients of \(x^{2}\) and \(y^{2}\)

$$
LATEXBLOCK1
$$

Step3: Complete the square for \(x\) and \(y\)

For \(x\): \((\frac{10}{2})^{2}=25\), for \(y\): \((\frac{8}{2})^{2}=16\)

$$
LATEXBLOCK2
$$

Step4: Divide by 324 to get standard form

$$
LATEXBLOCK3
$$

Answer:

The standard form of the ellipse is \(\frac{(x + 5)^{2}}{36}+\frac{(y + 4)^{2}}{9}=1\)