Analysis of an Ellipse needed

[MullenJohn]

Hello,
I am trying to enter an equation of an ellipse into my HP Prime and plot the equation and the determine the critical points of major and minor vertices, foci, center and eccentricity.

Would you know how to perform these steps with the HP Prime?

For example, I would like to plot the equation [(X-4)² / 16] + [(Y+1)²/25] = 1
After viewing the plot, I would like the calculator to show the major vertices (4,4) and (8, -1)
After viewing the plot, I would like the calculator to show the minor vertices (4,4) and (0, -1)
After viewing the plot, I would like the calculator to show the foci (4,2) and (4,-4)
After viewing the plot, I would like the calculator to show the eccentricity of 0.6
After viewing the plot, I would like the calculator to show the center (4, -1)
Cheers!