Problem: The graph of x2−4y2=0x^{2}-4 y^{2}=0x2−4y2=0 is:
Answer Choices:
A. a parabola
B. an ellipse
C. a pair of straight lines
D. a point
E. none of these Solution:
x2−4y2(x+2y)(x−2y)=0∴x+2y=0x^{2}-4 y^{2} \quad(x+2 y)(x-2 y)=0 \therefore x+2 y=0x2−4y2(x+2y)(x−2y)=0∴x+2y=0 or x−2y=0x-2 y=0x−2y=0. The graph of each equation is a straight line, so that the correct answer is (C)(C)(C)