Answer:
Center is at (0,0)
Step-by-step explanation:
An equation of ellipse in standard form is:
[tex]\displaystyle{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2} = 1[/tex]
Where center is at point (h,k)
From the equation of [tex]\displaystyle{x^2+5y^2-45=0}[/tex]. First, we add 45 both sides:
[tex]\displaystyle{x^2+5y^2-45+45=0+45}\\\\\displaystyle{x^2+5y^2=45}[/tex]
Convert into the standard form with RHS (Right-Hand Side) equal to 1 by dividing both sides by 45:
[tex]\displaystyle{\dfrac{x^2}{45}+\dfrac{5y^2}{45}=\dfrac{45}{45}}\\\\\displaystyle{\dfrac{x^2}{45}+\dfrac{y^2}{9}=1}[/tex]
Therefore, the center of ellipse is at (0,0) since there are no values of h and k.
