## Calculus (3rd Edition)

Ellipse: - the vertices are $(1\pm \frac{5}{2}, \frac{1}{5})$, $(1, \frac{1}{5}\pm1)$ - the foci are $(1\pm \sqrt{21/4},1/5)$ - the center is $(1,1/5)$
By completing the square, we can write the equation $$4 x^{2}+25 y^{2}-8 x-10 y=20$$ in the form $$4 (x-1 )^2+25 (y-\frac{1}{5})^2=25.$$ Then we get $$\left(\frac{x-1}{ 5/2}\right)^{2}+\left(\frac{y-\frac{1}{5}}{1}\right)^{2}=1$$ which is an ellipse with $a=5/2, b=1$ and hence $c=\sqrt{a^2-b^2}=\sqrt{21/4}$ So, we have: - the vertices are $(1\pm \frac{5}{2}, \frac{1}{5})$, $(1, \frac{1}{5}\pm1)$ - the foci are $(1\pm \sqrt{21/4},1/5)$ - the center is $(1,1/5)$