Question
Graph the circle 4x^2+4y^2-24x-16y-29=0
Answers
Reiny
You need the centre and the radius.
complete the square
4(x^2 - 6x + .....) + 4(y^2 - 4y + ....) = 29
4(x^2 - 6x + 9) + 4(y^2 - 4y + 4) = 29 + 36 + 16
4(x-3)^2 + 4(y-2)^2 = 81
divide by 4
(x-3)^2 + (y-2)^2 = 81/4
so the radius is 9/2 and the centre is (3,2)
complete the square
4(x^2 - 6x + .....) + 4(y^2 - 4y + ....) = 29
4(x^2 - 6x + 9) + 4(y^2 - 4y + 4) = 29 + 36 + 16
4(x-3)^2 + 4(y-2)^2 = 81
divide by 4
(x-3)^2 + (y-2)^2 = 81/4
so the radius is 9/2 and the centre is (3,2)