Question

The equation of a circle is x2 + y2 + 2x - 10y - 38 = 0. What are the coordinates of the

center and the length of the radius of the circle?

Answer 1

Centre = (-1, 5)

radius = 8units

Step-by-step explanation

The standard form of the equation of a circle is expressed as

x^2+y^2+2gx+2fy+C = 0

Center = (-g, -f)

radius = √g²+f²-C

Given the equation of a circle is x² + y²+ 2x - 10y - 38 = 0.

On comparing

2gx = 2x

2g = 2

g = 2/2

g = 1

2fy = -10y

2f =-10

f =-5

Centre = (-1, -(-5)) = (-1, 5)

radius = √1²+5²-(-38)

radius = √1+25+38

radius = √64

radius = 8units