Question

Which equation does the graph represent?x2 + y2 = 4x232+y242=1(x – 1)232+y242=1x242+(y+1)232=1

Answer 1

Given: The ellipse as shown in the image

To Determine: The equation of the the given ellipse

Solution

It can be observed that the ellipse is centered at origin

The general equation of a ellipse with center at origin is given as

For the ellipse with horizontal axis as the one given , the equation is

`(x^2)/(a^2)+(y^2)/(b^2)=1`

Let us apply this to the given

From the above, we see that a = 3, b = 4.

Hence, the equation of the given ellipse is

`(x^2)/(3^2)+(y^2)/(4^2)=1`