SOLUTION: Find the equation of circle with PQ as diameter if the line y = x/2 intersects ellipse {{{y^2}}} + {{{x^2/4 = 1}}} at the points P and Q?

The endpoints of the diameter are intersections of the line  y = x/2  with the ellipse   +  = 1.


To find these endpoints, substitute the line equation to the ellipse equation.


You will get intersection points  (x,y) = (,)  and  (x,y) = (,).


Thus the circle is centered at the origin of the coordinate system and has the radius of   = .


The standard equation of the circle is   +  = 2.5.    ANSWER