What is the radius x^2+y^2=3x+4y ?

The radius x^2+y^2=3x+4y is r= 5/2

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radius x^2+y^2=3x+4y

radius

x^{2} + y^{2} = 3 x + 4 y

r = \frac{5}{2}

Solution steps

x^{2} + y^{2} = 3 x + 4 y

Rewrite

x^{2} + y^{2} = 3 x + 4 y

in the form of the standard circle equation

(x - \frac{3}{2})^{2} + (y - 2)^{2} = (\frac{5}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{3}{2}, 2), r = \frac{5}{2}

And the radius is:

r = \frac{5}{2}

x^{2} + y^{2} - 10 x + 10 y + 49 = 0

x^{2} + (y - 1)^{2} = 64

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

x^{2} + y^{2} + 10 x - 6 y + 18 = 0

(x + 8)^{2} + (y + 5)^{2} = 3^{2}