What am I supposed to do with this problem..?

Question

If someone could help me figure out how to answer this problem and problems like it I would appreciate it. Here it is

Describe the graph of the equation
x^2+y^2+2x+2=0

Answer 1

well, to begin with, you can choose a range of values for x (say -2,-1,0,1,2).

put in these values one by one and get the corresponding values of y.

once that is done, you'll have pairs of x,y values.

on a sheet of graph paper, plot these points and join them to draw the graph of the equation.

Answer 2

When x = 0,

y^2 = -2
y = +/- sqrt (-2) = i * sqrt 2

where i = sqrt (-1)

When x = 0, a real number, y = i * sqrt 2, an imaginary number. In fact, if you substitute any value of x, y always turns out imaginary. Try it.

Can you find these values anywhere on the real y - axis on the Cartesian plane? NO.

So, this graph is imaginary. It cannot be drawn on the real Cartesian xy plane.