Question

convert the following equation for an ellipse to standard form.
16x² + 64y² - 1024 = 0
standard form

graph the ellipse.

Explanation:

Step1: Move the constant term to the other side

$$16x^{2}+64y^{2}=1024$$

Step2: Divide each term by the constant on the right - hand side

Divide each term of the equation \(16x^{2}+64y^{2}=1024\) by \(1024\).
For the \(x^{2}\) term: \(\frac{16x^{2}}{1024}=\frac{x^{2}}{64}\)
For the \(y^{2}\) term: \(\frac{64y^{2}}{1024}=\frac{y^{2}}{16}\)
So the equation becomes \(\frac{x^{2}}{64}+\frac{y^{2}}{16}=1\)

Answer:

The standard form of the ellipse is \(\frac{x^{2}}{64}+\frac{y^{2}}{16}=1\)