What is the maximum number of possible solutions for the system shown below? 3x2 + y2 = 64 x2 + y = 10 A. 1 B. 3 O c. 2 D. 4

The standard form of an equation of a circle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
(h, k) is the center
r is the radius
The first equation is that of a circle.
Now,
The second equation is,
[tex]\begin{gathered} x^2+y=10 \\ y=-x^2+10 \end{gathered}[/tex]This is an equation of a parabola (quadratic).
When a circle and parabola intersect (solution point), there can be maximum 4 solutions, or 4 intersecting points.
The graphs of the two equations are shown: