Question

What is the radius of a circle with the equation x2 + y2 – 14x + 10y = 250?

Answer 1

\(\normalsize\color{blue}{ x^2 + y^2 – 14x + 10y = 250 }\)

\(\normalsize\color{blue}{ x^2 – 14x+ y^2 + 10y = 250 }\)

\(\normalsize\color{blue}{ x^2 – 14x\color{red}{+49} + y^2 + 10y\color{green}{+50} = 250\color{red}{+49} \color{green}{+50} }\)

\(\normalsize\color{blue}{ x^2 – 14x-49+ y^2 + 10y +50= 349 }\)

\(\normalsize\color{blue}{ (x-7)^2 + (y+5)^2= 349 }\)

Answer 2

Compare \(\normalsize\color{black}{ (x-7)^2 + (y+5)^2= 349 }\) to

\(\normalsize\color{black}{ (x-h)^2 + (y-k)^2= r^2 }\)

Answer 3

x^2 + y^2 – 14x + 10y - 250=0
Equation is in the form of x^2 + y^2+2gx +2fy+c =0
Formula for radius r =sqrt(g^2+f^2-c)
2g= -14
g=-7
2f=10
f=5
r=sqrt((-7)^2+(5)^2+250)
=sqrt(49+25+250)
=18

source: http://www.mathskey.com/question2answer/