How do you graph # x^2+y^2-4x+10y+20=0#?

1 Answer
Jan 26, 2016

Answer:

Graphs a circle with centre #(2,-5)# and the radius #r=3#

Explanation:

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.

#x^2 -4x +y^2 +10y +20 =0#

Using completing the squares gives us
#(x-2)^2 -4 +(y+5)^2 -25 +20 = 0#

#(x-2)^2 +(y+5)^2 =9#

This is now in the form #(x-h)^2 + (y-k)^2 = r^2# where #(h,k)# is the centre and #r# is the radius.
therefore the centre is #(2,-5)# and the radius #r=3#

It is now possible to graph the circle.