Question

The equation below represents a circle.
x​2​ + ​y​2​ + 4​x​ – 2​y​ = ​a
Part A: What is the ​x​ coordinate of the center of the circle?
Part B: What is the ​y​ coordinate of the center of the circle?
Part C: What is the value of ​a​ in the equation if the radius of the circle is 8?

Answer 1

do you know how to complete the square?

Answer 2

no @welshfella I've never learned this stuff :/

Answer 3

@welshfella

Answer 4

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

you divide the coefficient of x by 2 - in this case its 4/2 = 2 so this gives(x + 2) ^2
when you expand that you get +4 so you have to subtract 4 so that its = to x^2 + 4x.

Answer 5

we intend to convert the equation of the circle to the standard form
(x - a)^2 + (y - b)^2 = r^2

here (a,b) is the center of circle and r = radius

Answer 6

so comparing
(x - a) and ( x + 2) we see that -a = + 2 give a = -2

so -2 is the x coordinate of the center of circle

Answer 7

now you can work out the y coordinate in a sismilar way by completing the square on
y^2 - 2y

Answer 8

try doing that

Answer 9

ok I will try

Answer 10

I'll start you off;-
y^2 - 2y
divide -2 by 2 = -1
so we have (x - 1)^2 - A

what will A be?

Answer 11

-1x^2=A @welshfella

Answer 12

no A willo be -1

because (x - 1)^2 = x^2 - 2x + 1 so to get this back to x^2 - 2x we have to subtract 1

Answer 13

oh

Answer 14

@welshfella whats y?