[tex](x+2)^{2}[/tex]+[tex](y-5)^{2}[/tex]= 34
The equation of a circle in standard form is
[tex](x-a)^{2}[/tex]+[tex](y-b)^{2}[/tex]=[tex]r^{2}[/tex]
where (a , b) are the coordinates of the centre and r is the radius
The centre is at the midpoint of the endpoints and the radius is the distance from the centre to either of the 2 endpoints
Using the midpoint formula
midpoint = [[tex]\frac{1}{2}[/tex](x[tex]x_{1}[/tex]+[tex]x_{2}[/tex], [tex]\frac{1}{2}[/tex]([tex]y_{1}[/tex]+[tex]y_{2}[/tex]
where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]=(3,8) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]=(-7,2)
centre = ([tex]\frac{1}{2}[/tex](3-7),[tex]\frac{1}{2}[/tex](8+2)) = (-2,5)
Calculate r using the distance formula
r = √([tex]x_{2}[/tex]-[tex]x_{1}[/tex])²+([tex]y_{2}[/tex]-[tex]y_{1}[/tex])²)
= √((3+2)²+(8-5)²) = √(25+9) = √34 ⇒ r² =(√34)² = 34
equation of circle is : (x+2)²+(y-5)² = 34
