Graph `x^2+4y^2=64` :

The standard form for an ellipse is `(x-h)^2/a^2+(y-k)^2/b^2=1` where the center of the ellipse is at (h,k). If a>b then the major axis of the ellipse is horizontal; if b>a the major axis is vertical.

Dividing by 64 we get:

`x^2/64+y^2/16=1` Since 64>16 the major axis is horizontal.

The length of the major axis is 2a; in this case it is 16. The length of the minor axis is 2b -- in this case 8. The center of the ellipse is at (0,0).

So the points (8,0),(-8,0),(0,4),(0,-4) lie on the ellipse. An easy way to sketch the ellipse is to lightly pencil in the rectangle formed by x=8,x=-8,y=-4,y=4; then sketch the ellipse inscribed in the recatangle.

The graph:

`x^2+4y^2=64` dividing for 64 we get:

`x^2/64+y^2/16=1` ellipse of axis `a=8` and `b=4`

Expilict form: `y=1/2sqrt(64-x^2)`

`y=0` `x= +-8` `x=0` `y=+-4`