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

The concept is to change the subject of formula.

Here we need to make y as the subject of formula.

The area, a, of an ellipse can be determined using the formula

a = πxy, $a =\pi  xy$

where x and y are half the lengths of the largest and smallest diameters of the ellipse.

Now we have to solve this equation for y.

Dividing both sides by $\pi x$ we get

$\frac{a}{\pi x }  =y$

or

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

Option D is the right answer.

Answer 2

We have to find an equation solved for y from the formula for the area of an ellipse:

a = Pi x y .

Here x stays for the half of the length of the largest diameter and y stays for the half of the length of the smaller diameter and Pi is approx 3.14.

We start with an original equation.

a = Pi x y ( then divide both sides by Pi x ).

a / ( Pi x ) = y; y = a : ( Pi x ).

Answer: D. y = a : ( Pi x ).

a=πxy  

aπ=xy

y=aπx