Question

Find the Centre and radius of
the
circle
x² + y² -x+2y-3 = 0​

Answer 1

Answer:

(X^2)-X+(Y^2)+2Y-3=0

=>(X^2)-2(X/2)+(1/4)-(1/4)+(Y^2)+2Y+1-1-3=0

=>{X-(1/2)}^2+(Y+1)^2-(1/4)-1-3=0

=>{X-(1/2)}^2+(Y+1)^2-(1/4)-4=0

=>{X-(1/2)}^2+(y+1)^2-(17/4)=0

=>{X-(1/2)}^2+(Y+1)^2=17/4

=>{X-(1/2)}^2+(Y+1)^2={(√17)/2}^2

So, Centre of the circle is (1/2,-1)

and Radius of the circle is (√17)/2.