Question

Find the center and radius for the circle defined by the equation: x2+y2+1/2x-2y-5=0.

Answer 1

x²+y²+1/2x-2y-5=0

x²+1/2x+y²-2y=5

x²+1/2x+1/16+y²-2y+1= 5+1/16+1

(x+1/4)²+(y-1)²= 6 + 1/16

(x+1/4)²+(y-1)²= 16/16 +1/16

(x+1/4)²+(y-1)²= 17/16

(x+1/4)²+(y-1)²=
`(\sqrt{ (17)/(16) } )^(2)`

(x+1/4)²+(y-1)²=
`( ( √(17) )/(4) ) ^(2)`

-> center of the circle= M(1/4 , -1)

-> radius=
`( √(17) )/(4)`