Question

question 1 of 10 what is the maximum number of intersection points a hyperbola and a circle could have? a. 2 b. 3 c. 4 d. 1

Explanation:

Step1: Recall equations

A hyperbola is a second - degree curve given by an equation of the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1$ (for a standard hyperbola) and a circle is a second - degree curve given by $(x - h)^{2}+(y - k)^{2}=r^{2}$.

Step2: Consider degree of equations

When we solve the system of equations of a hyperbola and a circle simultaneously, we get a system of two second - degree equations. The maximum number of solutions of a system of two second - degree equations is 4. Geometrically, a circle can intersect a hyperbola at up to 4 points.

Answer:

C. 4