Question

Which of the following nonlinear inequalities is graphed below

Answer 1

(x²/4) + (y²/16) ≤ 1

Explanation:

The general form of the ellipse in the graph is

x²/4 + y²/16 = 1

we want to find the inequality which represents the shaded area this will determine whether which of the following 2 choices are correct

Choice 1: x²/4 + y²/16 ≥ 1

Choice 2: x²/4 + y²/16 ≤ 1

we note that point (0,0) lies inside the shaded area. Which means if we substitute (0,0), it should create an equality that is valid.

try choice 1: 0²/4 + 0²/16 = 0 ≥ 1 (not valid because obviously zero is smaller than 1)

try choice 1: 0²/4 + 0²/16 = 0 ≤ 1 (this is valid, hence choice 2 is the answer)