Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.
x2 + 2x + y2 + 4y = 19

Answer 1

@ganeshie8

Answer 2

I've gotten this far idk what to do next
x2 + 2x + y2 + 4y = 19
(x2 + 2x) + (y2 + 4y) = 19

Answer 3

good progress, next is easy
just complete the square for each bracket

Answer 4

how do you do that

Answer 5

do u knw (a+b)^2 formula ?

Answer 6

no

Answer 7

sorry

Answer 8

its okay :)
here is the formula :-

(a + b)^2 = a^2 + 2ab + b^2

Answer 9

basically, we want to cookup the brackets into something like above

Answer 10

x2 + 2x + y2 + 4y = 19
(x2 + 2x) + (y2 + 4y) = 19

(x2 + 2*1*x) + (y2 + 2*2*y) = 19

Answer 11

fine wid above ?

Answer 12

so do you mulity them together to get the next step

Answer 13

yes, i just pulled the 2 out

Answer 14

next ima add 1^2 in first brac, and 2^2 in second brac

Answer 15

so itll be (x2 + 2x+2) + (y2 + 4y+ 4) = 19

Answer 16

x2 + 2x + y2 + 4y = 19
(x2 + 2x) + (y2 + 4y) = 19

(x2 + 2*1*x) + (y2 + 2*2*y) = 19

(x^2 + 2*1*x + 1^2) + (y^2 + 2*2*y + 2^2) = 19 + 1^2 + 2^2

(x+1)^2 + (y+2)^2 = 24

Answer 17

ive used (a+b)^2 formula in last step, above

Answer 18

let me knw once u digest above

Answer 19

so is that the final answer???
@ganeshie8

Answer 20

humm ased on above equation,
center = (-1, -2)
radius = sqrt(24)

Answer 21

Can you please help me with another question?

Answer 22

Stacy wants to construct a circle inscribed in a triangle while Ben wants to construct a circle circumscribed about a triangle. How will Stacy and Ben's steps differ from each other?

Answer 23

@ganeshie8