Question

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

(-7, -1), 36 units

(7, 1), 36 units

(7, 1), 6 units

(-7, -1), 6 units

Answer 1

\[x^2+14x+(\frac{14}{2})^2=(x+\frac{14}{2})^2 \text{ or after simplifying } (x+7)^2 \\ \text{ you try this part } \\ y^2+2y+(?)^2=(x+?)^2\]
what should the question mark be ?

Answer 2

7

Answer 3

how did you come to 7?

Answer 4

cut 14 in half

Answer 5

\[x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2\]

Answer 6

well you don't have 14 in front of y
you have a 2 in front of y
so why are you doing anything with 14?

Answer 7

right sorry

Answer 8

I actually did the x part for you

Answer 9

I'm looking for you to try the y part using the x part I did for you as an example

Answer 10

but in general if you have y^2+by+c
(you know if the coefficent of y^2 is 1)
you just do the following:
take the number in front of y....divide it by 2 and the square the result
and that is what you need to add to complete the square

Answer 11

so its 1

Answer 12

right since the number in front of our y is 2
and 2/2 is 1
and then 1^2 is 1

Answer 13

\[y^2+2y+1=(y+1)^2 \]

Answer 14

now what ever you add in to one side you need to add into the other

Answer 15

\[x^2+14x+y^2+2y=-14\]
this is the original problem

Answer 16

you added in 7^2 and 1^2 on the left hand side
you add need to do the same to the right hand side

Answer 17

\[(x+7)^2+(y+1)^2=-14+7^2+1^2\]

Answer 18

when you are ready you can simplify the left hand side

Answer 19

\[(x-h)^2+(y-k)^2=r^2 \text{ tells us } (h,k) \text{ is center and } r \text{ is radius }\]

Answer 20

so it d

Answer 21

that is right because you get r^2=36
and so r=6
and yes (h,k)=(-7,-1)

Answer 22

thank a lots

Answer 23

gtg