The ellipse is centered at the origin. The length of its horizontal axis is 8, and the length of the vertical axis is 6. What is the equation for the ellipse?

Question

This question is about ellipses          

Answer 1

An ellipse can be defined as the locus of all points that satisfy the equation

 

(x²/a²) + (y²/b²) = 1

where:
x,y are the coordinates of any point on the ellipse,
a, b are the radius on the x and y axes respectively,

 

So, in the case of this problem:

 

If the total length of the horizontal axis is 8, then the radius on the x axis is 4, and, if the total length of the y axis is 6, then the "radius" in the y direction is 3.

 

If I have interpreted the question correctly, then the equation should be

 

(x²/16) + (y²/9) = 1