Which graph represents the solution of x squared plus 9 y squared is less than or equal to 81 and y squared plus 2 is less than x ?

Answer

A

Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.

B

Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.

C

Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.

D

Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.

Explanation

The inequality x² + 9y² ≤ 81 describes the region inside an ellipse centered at (0, 0), with x-intercepts ±9 and y-intercepts ±3. The inequality y² + 2 < x is equivalent to x > y² + 2, so its solutions lie to the right of the parabola x = y² + 2—outside the parabola’s enclosed region. Choice D shows both regions combined.

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Systems of Inequalities — Quiz

Which graph represents the solution of x squared plus 9 y squared is less than or equal to 81 and y squared plus 2 is less than x ?

Explanation

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