Answer:
Yes, It is ellipse
Step-by-step explanation:
Given Equation : [tex]\dfrac{(x-5)^2}{3}+\dfrac{(y+1)^2}{5}=1[/tex]
The standard equation of ellipse
[tex]\dfrac{\left(x-h\right)^{2}}{a^{2}}+\dfrac{\left(y-k\right)^{2}}{b^{2}}=1[/tex]
If we compare the given equation with standard equation of ellipse. It would be same.
Yes, the given equation represents ellipse.
The center of ellipse (5,-1)
[tex]a=\sqrt3[/tex]
[tex]b=\sqrt5[/tex]
- If a>b then horizontal ellipse.
- If a<b then vertical ellipse.
For the given equation [tex]\sqrt3<\sqrt5\Rightarrow a<b[/tex]
Therefore, it is vertical ellipse.
Graph: Please find attachment
