What is (x-1)^2+(y+4)^2=25 ?

The solution to (x-1)^2+(y+4)^2=25 is Circle with (a,b)=(1,-4),r=5

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(x-1)^2+(y+4)^2=25

(x - 1)^{2} + (y + 4)^{2} = 25

(a, b) = (1, - 4), r = 5

Solution steps

(x - 1)^{2} + (y + 4)^{2} = 25

Rewrite

(x - 1)^{2} + (y + 4)^{2} = 25

in the form of the standard circle equation

(x - 1)^{2} + (y - (- 4))^{2} = 5^{2}

Therefore the circle properties are:

(a, b) = (1, - 4), r = 5

(x - 1)^{2} + (y + 4)^{2} = 16

2 x^{2} + 2 y^{2} + x - 6 = 0

x^{2} + y^{2} - 2 x + 2 y - 23 = 0

(x - 5)^{2} + (y - 2)^{2} = 25

(x + 2)^{2} + (y - 5)^{2} = 16

What is (x-1)^2+(y+4)^2=25 ?
The solution to (x-1)^2+(y+4)^2=25 is Circle with (a,b)=(1,-4),r=5