Question

When graphed, the circle with equation
x^2 +y^2 +4x -4y +7 =0
will lie ENTIRELY in Quadrant
A) I.
B) II.
C) III.
D) IV.

Answer 1

you can use desmos to graph

https://www.desmos.com/calculator

Answer 2

I have a standardized test coming up on Tuesday and I will not be able to use the website you recommended. Could you tell me the steps in graphing this equation?

Answer 3

alternate
group the x portion group the y portion find the value needed to complete each square
the center of the circle is (h,k) using (x-h)^2 + (y-k)^2 = r^2 r is the radius of the circle

Answer 4

x^2 +y^2 +4x -4y +7 =0

(x^2+4x) +(y^2 -4y) +7 =0

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focus on just the (x^2+4x) terms for now. What is needed here to complete the square?

Answer 5

a 4 is needed?

Answer 6

correct, you take half of the x coefficient 4 to get 2
then you square 2 to get 4

we add and subtract 4 so things stay balanced (effectively it's like adding 0)

x^2 + 4x

x^2 + 4x + 4 - 4

(x^2 + 4x + 4) - 4

(x+2)^2 - 4

Answer 7

so x^2 + 4x turns into (x+2)^2 - 4

Answer 8

what does y^2 - 4y turn into when we complete the square?

Answer 9

(y-2)^2 + 4

Answer 10

let's expand (y-2)^2 + 4 out


(y-2)^2 + 4

(y-2)(y-2) + 4

y(y-2) - 2(y-2) + 4

y^2 - 2y - 2y + 4 + 4

y^2 - 4y + 8


so we went from (y-2)^2 + 4 to y^2 - 4y + 8

but we wanted to go from (y-2)^2 + 4 to y^2 - 4y

Answer 11

y^2 - 4y

y^2 - 4y + 4 - 4

(y^2 - 4y + 4) - 4

(y-2)^2 - 4

If you expanded (y-2)^2 - 4 out and simplified, you would get y^2 - 4y again

Answer 12

So sorry! I've mistaken my -4 as +4

Answer 13

that's ok

Answer 14

after those completing the square steps for x and y, we will have


x^2 +y^2 +4x -4y +7 =0

(x^2+4x) +(y^2 -4y) +7 =0

(x+2)^2 - 4 + (y-2)^2 - 4 = 0


now you must get the equation into (x-h)^2 + (y-k)^2 = r^2 form

Answer 15

wait, where did the 7 go?

Answer 16

oh my bad lol

Answer 17

x^2 +y^2 +4x -4y +7 =0

(x^2+4x) +(y^2 -4y) +7 =0

(x+2)^2 - 4 + (y-2)^2 - 4 +7 = 0

Answer 18

would I write it like this: (x+2)^2 + (y-2)^2= 1 ?

Answer 19

that is correct

Answer 20

what is the center of that circle?

Answer 21

Thanks so much I know how to graph it from here!

Answer 22

you're welcome