Question

At how many points do the following curves intersect: \[ \frac{y^2}{9} - \frac{x^2}{16} = 1 \quad {and} \quad \frac{x^2}{4} + \frac{(y - 4)^2}{16} = 1 \]

• A. 0
• B. 1
• C. 2
• D. 4

Hint:

When solving systems involving conic sections, such as an ellipse and hyperbola, check the feasibility of their intersection by substituting one equation into the other.

Answer 1

The Correct Option is C

The first equation represents a hyperbola, and the second equation represents an ellipse. To find the number of intersection points, we need to solve the system of equations by substituting one into the other and analyzing the resulting equation. 
After solving the system, we find that there are 2 points of intersection. 
Thus, the correct answer is \( \boxed{2} \).