Answer:
![(-11,0)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8k4vieoozfldg20jgp0uqfi8igp2ffhswq.png)
and
![(11,0)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8rq0rvh9l04mqhkcuokb3kpwpjdkrzpgxh.png)
.
Explanation:
The given ellipse has the equation:
![(x^2)/(121)+(y^2)/(1)=1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/woc921ir1jcjgkh1kh6q5xt3drddnavrcj.png)
This can be rewritten as
![(x^2)/(11^2)+(y^2)/(1^2)=1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/vt2buv3m6jcqz2lku63khsmbkxmxfrypg2.png)
We compare this to the general equation of the ellipse:
![(x^2)/(a^2)+(y^2)/(b^2)=1](https://img.qammunity.org/2020/formulas/mathematics/high-school/o17jum9zosp8f9ha4roicvrljxxbicbflv.png)
We have
![a=11](https://img.qammunity.org/2020/formulas/mathematics/middle-school/y1knmo142izc95oew6yoyd96bb4ou746t5.png)
and
![b=1](https://img.qammunity.org/2020/formulas/mathematics/high-school/hq718e7r8c46v6y7iqg603qgctwgv9798j.png)
The vertices of this ellipse are at
![(-a,0)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/y7pb6z3jjru11zfpknzjl6z1kz5tsr7jqq.png)
and
![(+a,0)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/iswf7p0a9s3ec57v1nawy8z0d77h80bivf.png)
.
Therefore the vertices of this ellipse are at
![(-11,0)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8k4vieoozfldg20jgp0uqfi8igp2ffhswq.png)
and
![(11,0)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8rq0rvh9l04mqhkcuokb3kpwpjdkrzpgxh.png)
.
The correct choice is A.