Question

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

Answer 1

The standard form of an equation of a circle is,

`(x-h)^2+(y-k)^2=r^2`

Where

(h, k) is the center

r is the radius

The first equation is that of a circle.

Now,

The second equation is,

`\begin{gathered} x^2+y=10 \\ y=-x^2+10 \end{gathered}`

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: