Question

HELP!!!!!

Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths.
x2 + y2 − 2x + 2y − 1 = 0
x2 + y2 − 4x + 4y − 10 = 0
x2 + y2 − 8x − 6y − 20 = 0
4x2 + 4y2 + 16x + 24y − 40 = 0
5x2 + 5y2 − 20x + 30y + 40 = 0
2x2 + 2y2 − 28x − 32y − 8 = 0
x2 + y2 + 12x − 2y − 9 = 0

Answer 1

the general equation of circle is

x^2 + y^2 + 2gx + 2fy + c = 0

compare your equations withe above to find the values of g, f and c
the radius of the circle will be sqrt(g^2 + f^2 - c)

Answer 2

for example the radius of first one is sqrt(1^2 + (-1)^2 - (-1)) = sqrt 3

Answer 3

but its asking for assending radius form

Answer 4

or their radius lengths

Answer 5

yes well find the radii of all 7 equations first then you can arrange them in the correct order

Answer 6

do you see how i got g = 1 and f = -1?

Answer 7

and c = -1