Provide an appropriate response. -Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$-intercepts at $- 2$ and 2 , and $y$-intercepts at 3 and $- 3$ ? A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } 1$ B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 }

Question

Provide an appropriate response.
-Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$-intercepts at $- 2$ and 2 , and $y$-intercepts at 3 and $- 3$ ?
A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } > 1$
B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } < 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } < 1$
D) $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 3 } < 1$

Quizplus · Accepted Answer

The equation of an ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ and $2b$ are the lengths of the major and minor axes, respectively. Given the $x$-intercepts are $-2$ and $2$, $a = 2$, and given the $y$-intercepts are $-3$ and $3$, $b = 3$. Therefore, the equation becomes $\frac{x^2}{2^2} + \frac{y^2}{3^2} = 1$. The inequality that represents the region inside this ellipse is $\frac{x^2}{4} + \frac{y^2}{9} < 1$.

Provide an Appropriate Response xxx -Intercepts At −2- 2−2 And 2 , And

Provide an Appropriate Response $x$ -Intercepts At $- 2$ And 2 , And