How to find the center and radius of the circle x^2+y^2-6x+8y=0?

Ean Chapman

Ean Chapman

Answered question

2023-03-23

How to find the center and radius of the circle x 2 + y 2 - 6 x + 8 y = 0 ?

Answer & Explanation

awesomeamber802x

awesomeamber802x

Beginner2023-03-24Added 8 answers

the equation of a circle in standard form is
| 2 2 ( x - a ) 2 + ( y - b ) 2 = r 2 2 2 | ̲ ¯
where ( a , b ) are the coordinates of the centre and r
is the radius
use the method of completing the square
on both the x and y terms
x 2 - 6 x + y 2 + 8 y = 0
x 2 + 2 ( - 3 ) x + 9 + y 2 + 2 ( 4 ) y + 16 = 0 + 9 + 16
( x - 3 ) 2 + ( y + 4 ) 2 = 25 in standard form
centre = ( 3 , - 4 ) and radius = 25 = 5

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