Answer:
[tex](x-1)^2+(y-2)^2=6.25[/tex]
Step-by-step explanation:
The equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
The center is the red dot, which is (1,2). Thus, h=1 and k=2.
To find the radius, you need to use the distance formula. We are given two coordinates: the center (red dot) at (1,2) and a blue dot on the circle at (2.5,4). Find the radius by using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let (1,2) be x₁ and y₁ and let (2.5,4) be x₂ and y₂. Therefore:
[tex]d=\sqrt{(2.5-1)^2+(4-2)^2}\\d=\sqrt{(1.5)^2+2^2}\\d=\sqrt{2.25+4}\\d=\sqrt{6.25}=2.5[/tex]
Thus, r is 2.5.
Plugging these numbers into the equation, we have:
[tex](x-h)^2+(y-k)^2=r^2\\(x-1)^2+(y-2)^2=2.5^2\\(x-1)^2+(y-2)^2=6.25[/tex]
