Question

What is the maximum number of possible solutions for the system shown

below?

х2 – 4у2 = 16
x2+y2 = 36

А. 2
B. 4
C. 3
D. 1

Answer 1

4

Explanation:

х^2 – 4у^2 = 16 is the equation of a hyperbola with center at the origin. Parts of this graph show up in all four quadrants.

Similarly, x^2 + y^2 = 36 is the equation of a circle with center at the origin); the graph shows up in all four quadrants.

So there is an intersection of the graphs in all four quadrants. Therefore, 4 is the maximum number of possible solutions of the system shown.