If the circle x square + y square +ax + 2y + 4=0. passes through (2,2) find the centre of the circle.

factor: x^2+y^2+ax+2y+4=0

First plug in the point (2,2) into the equation to find "a".

2^2+2^2+a(2)+2(2)+4=0

2a=-16

a=-8

So now with the value of a we have:

x^2+y^2-8x+2y+4=0

Let rearrange the terms:

x^2-8x+y^2+2y+4=0

Move the constant over to the right side of the equation.

x^2-8x+y^2+2y=-4

Completing the square is tricky but what needs to be done.

x^2-8x+16+y^2+2y+1=13

And then factor the sum and differences of squares.

(x-4)^2+(y+1)^2=13

Divide by 13.

(x-4)^2/13+(y+1)^2/13=0

Now it is in factored form, so we can get the center of the circle.

The center will be at (4,-1).

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00