Finds out the center & radius of each of the following circles & sketch the graph of the circle.
a) x^{2}+ y ^{2} = 1
b) x^{2}+ ( y - 3)^{2 } = 4
Solution
In all of these all that we actuallyhave to do is compare the equation to the standard form and recognizes the radius & center. Once that is done determine the four points talked about above and sketch in the circle.
x^{2}+ y ^{2} = 1
In this case it's just x & y squared by them. The only way which we could have it is to have both h & k be zero. Thus the center & radius is,
center = (0, 0) radius =√1 = 1
Don't forget that the radius is the square root of the number on the other side of the equal sign. Following is a sketch of this circle.