How do you graph # x^2+y^2-4x+10y+20=0#?
Graphs a circle with centre
This equation can be recognised as the equation of a circle - see Conic sections for a description of the patterns of the conic equations.
We need to reorganise and simplify it in order to get it into the standard form for a circle that will give us the centre and radius, after which it will be very easy to graph.
Using completing the squares gives us
This is now in the form
therefore the centre is
It is now possible to graph the circle.