determine the center and radius of a circle x^2+y^2 +16x-22y-20=0?

Answer 1

x^2 + 16x + y^2 -22y = 20

Complete the square for x and y:

x^2 + 16x + 64 + y^2 -22y + 121 = 20 + 64 + 121

Factor:

(x+8)^2 + (y-11)^2 = 205

Center is (-8, 11) and radius = sqrt (205)

Answer 2

You need to get the equation in the standard form for a circle which is:

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

where the center of the circle is at (h,k) and the radius of the circle = r.

In order to rearrange the equation, you will need to complete the square and factor....

Rewrite it as:

x^2 + 16x + y^2 - 22y = 20

If you don't remember how to complete the square be sure to review your notes and/or textbook. The idea is to add a number to both sides of the equation so that you can factor the expression and end up with something in the form of (x - h)^2 and (y - k)^2.

So for x^2 + 16x you would add to both sides (16/2)^2 = 64 and for y^2 - 22y you would add to both sides (22/2)^2 = 121

(x^2 + 16x + 64) + (y^2 - 22y + 121) = 20 + 64 + 121

Remember in the step above you have to add to both sides in order to keep the equation balanced/equal.

Factor left side & simplify right:

(x + 8)^2 + (y - 11)^2 = 205

Now you just need to use what you know from the standard form to determine the center & radius... Remember that it's in the form (x - h)^2 + (y - k)^2 = r^2 so you need to be careful that you get the sign right on the coordinates for the center (h, k)... if h & k are added to x & y then they are actually negative. Similarly, don't forget the left side is r^2 so you need to take the square root to determine r.

Answer 3

xsq+ysq+16x-22y-20=0

Compare with

xsq+ysq+2gx+2fy+c=0 ...Standard equation of circle

g=8
f=-11
c=-20

Centre O(-g,-f)=(-8,11)

Radius r =sqroot(gsq+fsq-c)
r=sqroot(64+121+20)
r=sqroot(205)

Answer 4

umm...What are the ^?, otherwise i could probably solve it...without those... it'd be somewhere close to 18x-20y=20?

...then again, i'm only in 8th grade algebra so...