jmc

Question

The equation x^236 + (y+5)^216 = 0describes a degenerate ellipse, because the right-hand side is 0 instead of 1 (as in the standard form for an ellipse). Of all the points on the graph of this equation, what is the largest possible y-coordinate?

Accepted Answer

Note that the equation is a sum of squares equaling 0, which is only possible if both squares are zero. That is, we must have x^236 = 0 and (y+5)^216 = 0,which implies that x=0 and y=-5. Since (x,y)=(0,-5) satisfies the given equation, it is the only point on the graph of this equation, so the answer is -5.