Question

The graphs of the conics intersect at two points.

x² + y² = 9
x²/9 − y²/4 = 1

What are the coordinates of these points of intersection?

Answer 1

To find the coordinates of the points of intersection, solve the system of equations by substituting one equation into the other.

Step-by-step explanation:

The given system of equations represents the conic sections of a circle and a hyperbola. To find the coordinates of the points of intersection, we can solve the system of equations. First, we rewrite the second equation to match the format of the first equation: x² + y² = 9x²/9 - y²/4 = 1. Next, we substitute the expression for y² from the first equation into the second equation: x² + (9x² - 9)²/9 - y²/4 = 1. By simplifying and rearranging terms, we can solve the system to find the x-values and then substitute them back into either equation to find the corresponding y-values of the points of intersection.