Question

What is the value of (256x square16/81y squre4)square-1/4 .

Answer 1

The Standard Form of an Ellipse Centered at The Origin

Recall that the equation of a circle centered at the origin has equation

        x2 +  y2  =  r2

where r is the radius. Dividing by r2 we have

        x2             y2   
                +               =   1                
        r2             r2

for an ellipse there are two radii, so that we can expect that the denominators should be different.  Hence we have the standard form of an ellipse centered at the origin:

        x2             y2   
                +               =   1                
        a2             b2

 

The points (a,0), (-a,0), (0,b), and (0,-b) are called the vertices of the ellipse.

Note:  Although we have written the a below the x and the b below the y, it is customary to let a be the larger of the two and b be the smaller.