Question

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse.

Which is an equivalent equation solved for y?

y = a · πx
y = a + (πx)
y = a – πx
y = a ÷ (πx)

Answer 1

To solve the equation \( a = \pi xy \) for \( y \), we start with the original equation:

\[
a = \pi xy
\]

Next, we want to isolate \( y \). We'll divide both sides of the equation by \( \pi x \):

\[
y = \frac{a}{\pi x}
\]

This doesn't directly match any of the provided options, but let's look at the options more closely:

1. \( y = a · \pi x \)
2. \( y = a + (\pi x) \)
3. \( y = a - \pi x \)
4. \( y = a ÷ (\pi x) \)

The fourth option, \( y = a ÷ (\pi x) \), is equivalent to our derived equation \( y = \frac{a}{\pi x} \).

Thus, the equivalent equation solved for \( y \) is:

\[
\boxed{y = a ÷ (\pi x)}
\]