Math Help Forum: Graphing Circles

Alright, I don't know how to exactly describe these equations, but I know they look like a circle. So how would I be able to graph these? Doesn't say in my textbook sadly...

x^2+y^2 = 1

x^2+y^2=2

x^2+y^2 < or = to 3

x^2+y^2=0

Do you just draw the 1st circle with a radius of 1, and then the 2nd circle with a radius of square root of 2 (1.412...), then the next one with a radius of square root of 3, and then the last one is no circle?

You are correct for the first two. Since the third one is the circle is actually shaded in since all the values inside the circle are < the radius

The fourth is the circle of radius zero, which is just the point (0,0)


In general, to graph mark the center point (h,k) and then go out r units (which is the length of the radius) and draw the circle like that

Originally Posted by A Beautiful Mind

Alright, I don't know how to exactly describe these equations, but I know they look like a circle. So how would I be able to graph these? Doesn't say in my textbook sadly...

x^2+y^2 = 1

x^2+y^2=2

x^2+y^2 < or = to 3

x^2+y^2=0

Do you just draw the 1st circle with a radius of 1, and then the 2nd circle with a radius of square root of 2 (1.414...),

then the next one with a radius of square root of 3 ... set is all points on or inside the circle

, and then the last one is no circle?

point at the origin

...

as have been shown by the above poster,

the standard equation of a circle is (x - h)^2 + (y - k)^2 = r^2,

where (h,k) is the coordinate of the center, and r is the radius, i will plot with r = 1 and r = 3 and (h,k) as (0,0), obviously, the center is at thas examplese origin

here is another example with (h,k) equal (2,3) and r = square root of 2, with a graph

x^2+y^2=0 --> (x - 0)^2 + (y - 0)^0 = (0)^2

it is known as POINT CIRCLE, r = 0, center (0,0)

if r<0, the circle is known as DEGENERATE CIRCLE