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

1 Answer
Jul 28, 2016

This is a circle with centre (1, 2) and radius 5.

Explanation:

Complete the square for both x and y ...

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

= color(blue)(x^2-2x+1)+color(green)(y^2-4y+4)-25

= (x-1)^2+(y-2)^2-5^2

Add 5^2 to both ends and transpose to get:

(x-1)^2+(y-2)^2=5^2

This is in the form:

(x-h)^2+(y-k)^2=r^2

the equation of a circle with centre (h, k) = (1, 2) and radius r=5

graph{((x-1)^2+(y-2)^2-25)((x-1)^2+(y-2)^2-0.01) = 0 [-9.04, 10.96, -2.76, 7.24]}