Question

An equation of a circle is x^2 + y^2 – 10x + 6y + 18 = 0.

Part 1: Show all your work in determining the center and radius of this circle. (3 points)

Part 2: In complete sentences, explain the procedure used. (3 points)

Answer 1

@satellite73

Answer 2

@nincompoop

Answer 3

@ganeshie8

Answer 4

you need to factor the equation you have into this format:
(x + a)^2 + (y + b)^2 = z^2

Answer 5

I don't understand how to do that.... Can you help me?

Answer 6

complete the square, do you know that?

Answer 7

I don't remember all of it...

Answer 8

group the like terms together and I like the constant on the right of the equals

Answer 9

for the x portion, take half of the -10x term and square it

Answer 10

Sure! when you multiply a binomial like (x + a)^2 you get an x^2 term, a 2a*x term and an a^2 term.

You need to look for a way to divide the original eq's x^1 term in half

Answer 11

and do the same for the y variable. Look at (y + b)^2 and try to find the factor b that doubles to get 6y

Answer 12

so that would be x^2-10x+25, but since you're adding 25 to the left hand side you need to do that to the right as well. then x^2-10x+25 is written as (x-5)^2

Answer 13

\[x^2-10x+25+y^2+6y=-18+25\]=\[(x-5)^2+y^2+6y=7\] then do that for the y terms

Answer 14

take half of the 6y term and square it then add that number to the right side as well
\[(x-5)^2+(y+3)^2=16\]

Answer 15

are you following this lol?

Answer 16

so we add 9 to the right side?

Answer 17

yeah, that's how we got 16. so now that it is in the general form for a circle, what is the center and radius?

Answer 18

center is (5,-3) and the radius is 4?

Answer 19

A+

Answer 20

yay! Now can you help me put it into sentences? That's the other part....

Answer 21

well, tell me what we did

Answer 22

We rewrote the x part of the equation using completing the square. Then, the same with the y part. Then, we got the center from the x and y parts and the radius from the square root of the term to the right of the equal sign

Answer 23

but I have to make that sound better lol

Answer 24

you did pretty good though. I would say something like "We completed the square to get it in the form (x-h)^2+(y-k)^2=r^2, which is the general form of a circle where the center is at (h,k) and radius r.......