Conic Sections And Intersection Of Curves

Step 1: Rewrite the given equation.
The given equation is: Rearranging the terms:

Step 2: Complete the square for the -terms.
To complete the square for the -terms, add and subtract : This simplifies to:

Step 3: Recognize the difference of squares.
We now have a difference of squares: Taking square roots on both sides: So, we have two equations:

Step 4: Solve the system of equations.
For , we have: For , we have:

Step 5: Conclude the solutions.
Thus, the points of intersection are given by the equations and .

Final Answer: The points of intersection are the solutions to the equations and .