Question

Find the center and radius of the circle with equation x2 + y2 -2x + 4y - 11 = 0

Answer 1

\[x^2+y^2 -2x +4y-11=0 \]make perfect squares\[x^2-2x+1+y^2+4y+4-11=1+4\]now write the equation like this-\[(x-1)^2 + (y+2)^2 -11=5\]\[(x-1)^2 + (y+2)^2 = 16\]\[(x-1)^2 + (y+2)^2 =4^2\] we know the standard form of equation of a circle -\[(x-h)^2 +(y-k)^2 = r^2\]where the cordinates of centre are(h,k) and r is the radius so compring we get the centre as - (1,-2) and radius =4