SOLUTION: Rewrite the relation as a conic in standard form, then sketch the graph of the relation. {{{ 2x=sqrt( 8y-y^2 ) }}}

2x =    ====>  square both sides  ====>

 =  ====>  collect all retms in the left side  ====>

 = 0  ====> Complete the square in the group of y-terms  ====>

 +  = 16  ====>  Divide both sides by 16  ====>

 +  = 1.


You got the standard equation of an ellipse.


The major axis is parallel to y-axis and is vertical.
The minor axis is parallel to x-axis and is horizontal.

The major semi-axis has the length of 4 units.
The minor semi-axis has the length of 2 units.

The ellipse is taller than wide.

The center is at the point (x,y) = (0,2).

The linear eccentricity is  =  = .

The foci are at the points (,)  and  (,)