Answer: [tex](x-5)^2+(y-3)^2=18[/tex]
Step-by-step explanation:
Here, the endpoints of the diameter of a circle are (8, 6) and (2, 0),
The center of the circle = Mid point of the line segment that shows the diameter
= Mid point of (8, 6) and (2, 0),
= [tex](\frac{8+2}{2}, \frac{6+0}{2})[/tex]
= [tex](\frac{10}{2},\frac{6}{2})[/tex]
= ( 5, 3 )
Now, the diameter of the circle = Distance of the points (8,6) and (2,0)
= [tex]\sqrt{(2-8)^2+(0-6)^2}[/tex]
= [tex]\sqrt{6^2+6^2}[/tex]
= [tex]\sqrt{36+36}=\sqrt{72}=6\sqrt{2}[/tex] unit
⇒ The radius of the circle = 3√2 unit
Since, the standard form equation of the circle is (x-h)² + (y-k)² = r²
Where (h,k) is the center of the circle and r is the radius of the circle,
Hence, The standard form of the given circle is,
[tex](x-5)^2+(y-3)^2=(3\sqrt{2})^2[/tex]
[tex]\implies (x-5)^2+(y-3)^2=18[/tex]
