Plot ellipse from equation (no foci/axes)

I have an equation for an ellipse: x^2+y^2-4x-8y+10-2*log(2) = 0. How an I plot this in Matlab? Everything that I've found searching only tells how to plot if you have the foci and major/minor axes. I tried putting the equation into Wolfram Alpha, which gave me two expressions for y, but apparently that results in some complex values over the range [-4,4] for x. What else can I try?

Answer 1

[Andrew Newell]

One approach is to use ezplot:

ezplot('x^2+y^2-4*x-8*y+10-2*log(2)')

By default, this plots over the domain -2π < x < 2π, -2π < y < 2π. But you'll see that needs adjusting. Add axis limits:

ezplot('x^2+y^2-4*x-8*y+10-2*log(2)',[-2 6 0 8])

Finally, type

axis equal

and you'll see that it's actually a square.

An alternative is that you can complete the square (see, e.g., Completing the Square: Ellipse Equations), getting (x-2)^2+(y-4)^2=10+2*log(2). This is a circle with center at (2,4) and radius sqrt(10+2*log(2)) (about 3.4).

Answer 2

[proy]

Use Ellipse Calculator to find foci and major/minor axes from equation.

Answer 3

[Nicolas Flamant]

I recommend to use

fimplicit

which is now preferred to

ezplot