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?

Answer 1

An equivalent equation solved for y is  $y=\frac{a}{\pi x}$.  

Step-by-step explanation:

We are given that the area, a, of an ellipse can be determined using the formula a = πxy.

And we have to find an equivalent equation solved for y.

The given area formula for the ellipse, a = $\pi xy$

where, x is the half of the lengths of the largest diameters and y is the half of the lengths of the smallest diameters.

So, according to the question;

                    $a=\pi xy$

Moving $\pi$ to the left side of the equation;

                    $\frac{a}{\pi}= xy$

Now, moving x to the left side of the equation;

                     $\frac{a}{\pi x}= y$

Hence, an equivalent equation solved for y is  $y=\frac{a}{\pi x}$.