write the equation of the circle in standard form. Identify the radius and center. x^2+y^2-4x+6y+9=0

Question

X²+y²-4x+6y+9=-

 

Answer 1

(x-a)² + (y-b)² = r² , this is the standard form equation of a circle of radius r and center (a, b)

 

x²+y²-2ax-2by=r²-a²-b²  ⇒ -2a=-4 yields a=2 ; -2b=6 yields b=-3 ; r²-a²-b²=-9 ⇔ r²-4-9=-9 ⇒ r=2

 

Radius r=2

Center (2,-3)

 

(x-2)²+(y+3)² = 4