Problem: The number of distinct points common to the curves x2+4y2=1 and 4x2+y2=4 is:
Answer Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Solution:
Both curves are ellipses with the centers at the origin. The first, 12x2​+(21​)2y2​=1, has x-intercepts +1 and −1 , and y-intercepts +21​ and −21​. The second, 12x2​+22y2​=1, has x-intercepts +1 and -1 , and y-intercepts +2 and −2 . The number of distinct points of intersection is 2.