Question

question 18 of 30
what is the maximum number of intersection points a hyperbola and an ellipse could have?
a. 4
b. 2
c. 3
d. 0

Explanation:

Step1: Recall curve - intersection concept

The equations of a hyperbola and an ellipse are second - degree equations in two variables \(x\) and \(y\). When we find the intersection points of two curves, we solve their equations simultaneously. A system of two second - degree equations in two variables can have at most 4 solutions.

Step2: Visualize or use algebraic reasoning

Geometrically, we can think about the possible ways a hyperbola (which has two branches) and an ellipse (a closed curve) can intersect. They can cross each other at multiple points. The maximum number of times they can cross is when the equations representing them result in a fourth - degree polynomial equation (from substituting one equation into the other), and all the roots of that polynomial are real.

Answer:

A. 4