Respuesta :
ANSWER:
The intercepts are:
[tex]\begin{gathered} \text{ x-intercept} \\ -2,2 \\ \text{ y-intercept} \\ -3,3 \end{gathered}[/tex]The domain is:
[tex]D=\mleft\lbrace-2,2\mright\rbrace[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the intercepts and the domain as follows:
We must write the equation, in its ellipse form with its center outside the origin
[tex]\begin{gathered} 9x^2\: +\: 4y^2\: =\: 36 \\ \text{The form is:} \\ \frac{(x-h)^2}{a^2}+\: \frac{(y-k)^2}{b^2}\: =\: 1 \\ \text{now,} \\ \frac{9}{36}(x-0)^2\: +\: \frac{4}{36}(y-0)^2\: =\: \frac{36}{36} \\ \frac{x^2}{4}\: +\frac{y^2}{9}=\: 1 \\ \frac{x^2}{2^2}\: +\: \frac{y^2\: }{3^2}=\: 1 \\ a=2 \\ b=3 \end{gathered}[/tex]Therefore,
The intercepts are:
[tex]\begin{gathered} \text{ x-intercept} \\ -2,2 \\ \text{ y-intercept} \\ -3,3 \end{gathered}[/tex]And the domain that are the input values would have the following interval:
[tex]D=\mleft\lbrace-2,2\mright\rbrace[/tex]