Question

What is the radius of a circle
x^2 + y^2 +8x -10y -9 =0

Answer 1

compare with
\[x^2+y^2+2gx+2fy+c=0\]
2g=8,g=4
2f=-10
f=-10/2=-5
centre is(-g,-f)
i.e.,(-4,5)
or complete the squares and compare with
\[(x-h)^2+(y-k)^2=r^2,centre~ is ~ (h,k)\]

Answer 2

Would the correct answer be
5 [\sqrt{2}\]@surjithayer

Answer 3

@surjithayer

Answer 4

by one method centre is (-4,5)
and radius=\[\sqrt{g^2+f^2-c}=\sqrt{\left( -4 \right)^2+\left( 5 \right)^2-(-9)}=\sqrt{16+25+9}=\sqrt{50}=5\sqrt{2}\]
you are correct.