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Decide whether or not the equation has a circle as its graph. If it does, give the center and the radius. If it does not, des
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Answer #1

The general equation of a circle is

(x -h )^2 + (y - k )^2 = r^2

where (h, k) is the center and r is the radius

x^2 + y^2 + 4x - 8y + 24 = 0

=> x^2 + 4x + y^2 - 8y + 24 = 0

=> (x^2 + 2x(2) + (2)^2 - (2)^2) + (y^2 - 2y(4) + (4)^2 - (4)^2) + 24 = 0

=> (x^2 + 2x(2) + (2)^2 )- (2)^2 + (y^2 - 2y(4) + (4)^2 )- (4)^2 + 24 = 0

=> (x + 2 )^2- 4 + (y - 4 )^2- 16 + 24 = 0

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

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

Since, r^2 = -4 is not possible for any real value of r

Therefore,

The graph is nonexistent.

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