Question

If A = {(x, y)/x^2 + y^2 = 25} and B{(x, y)/x^2 + 9y^2 = 144} then A ∩ B contains how many points.

Answer 1

since y^2 = 25-x^2, we have

x^2 + 9(25-x^2) = 133
x^2 = 33/2
So, since both curves are symmetric about (0,0), A ∩ B has 4 points -- one in each quadrant.

Answer 2

thank u sir.