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# equation of a circle

write the equation of the circle x2+y2-6x+8y=0 in the standard form. Find the radius of the circle and the distance from the center to the origin

### 2 Answers by Expert Tutors

Ralph L. | Algebra I, II, Visual Basic, Beginning C++ tutorAlgebra I, II, Visual Basic, Beginning C...
4.0 4.0 (1 lesson ratings) (1)
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x2 + y2 - 6x + 8y = 0

rearrange the equation:

x2 - 6x + y2 + 8y = 0

we use completing the square:

(x - 3)2 + (y + 4)2 = 9 + 16 = 25

so, radius is √25 or 5

also, distance from center to origin is also 5

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
1
(a ± b)2 = a2 + 2ab + b2

Standard form for the equation of the circle is
(x -a)2 + (y - b)2 = r2

Distance between two poins on the coordinate plane is:
d = √[(x1 - x2)2 + (y1- y2)2]

~~~~~~~~~~~

x2 + y2 - 6x + 8y = 0

(x2 - 2*3*x + 9) + (y2 + 2*4*y + 16) = 9 + 16

(x - 3)2 + (y + 4)2 = 52

and coordinates of the central are (3, - 4) and coordinates of origin are (0, 0), the
distance from the central to the origin is:

d = √(x2 + y2) = √25 = 5