A nonlinear system has equations whose graphs may curve. When the question asks how many ordered pairs satisfy a circle and a parabola, graph both equations in Desmos and count their intersections: each shared point satisfies both equations. Keep the entire circle in view. An intercept on only one graph isn't a solution, and the squared terms don't automatically give four solutions.
Hints
- Hint 1
In circle standard form, , the center is and the radius is . Read those from the first equation. How far does the circle reach in each direction?
- Hint 2
An intersection is a point shared by both graphs, so its coordinates satisfy both equations. Graph the parabola alongside the circle, and check the lower half as carefully as the upper half.
Step-by-step
Graph and count intersections
Step 1Read the circle's size and position
The first equation matches the standard form . So the center is , and the radius is because .
- Step 2
Show the whole circle
Type in Desmos. The circle reaches from to and from to . Use the window shown to see the entire circle; any solution must lie on it.
- Step 3
Count the shared points
Add , then click the two crossings. Desmos shows and approximately . Each crossing is one ordered pair that makes both equations true. So exactly ordered pairs satisfy the system. Choice B.