Answer: a. Radius of circle = [tex]\sqrt{85}[/tex]
b. The equation of this circle : [tex](x-3)^2+(y-10)^2=85[/tex]
Step-by-step explanation:
Given : Center of the circle = (3,10)
Circle is passing through (12,12).
a. To find the radius we apply distance formula (∵ Radius is the distance from center to any point ion the circle.)
Radius of circle = [tex]\sqrt{(12-3)^2+(12-10)^2}[/tex]
Radius of circle = [tex]\sqrt{(9)^2+(2)^2}=\sqrt{81+4}=\sqrt{85}[/tex]
i.e. Radius of circle = [tex]\sqrt{85}[/tex]
b. Equation of a circle = [tex](x-h)^2+(y-k)^2=r^2[/tex] , where (h,k)=Center and r=radius of the circle.
Put the values of (h,k)= (3,10) and r= [tex]\sqrt{85}[/tex] , we get
[tex](x-3)^2+(y-10)^2=(\sqrt{85})^2[/tex]
[tex](x-3)^2+(y-10)^2=85[/tex]
∴ The equation of this circle :[tex](x-3)^2+(y-10)^2=85[/tex]
