Answer:
Center = (1, -3)
Radius = 5.1
Equation: (x-1)² + (y+3)² = 26
Explanation:
Taking into account the figure, we can say that the center of the circle is the point (h, k) = (1, -3)
Then, to calculate the radius of the circle, we need to find the distance between the points (1, -3) and (2, 2).
So, the distance between two points (x1, y1) and (x2, y2) can be calculated as:
[tex]\text{Distance = }\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Replacing (x1, y1) by (1, -3) and (x2, y2) by (2, 2), we get that the distance or radius of the circle is equal to:
[tex]\begin{gathered} \text{Distance = }\sqrt[]{(1-2)^2+(-3-2)^2} \\ \text{Distance}=\sqrt[]{(-1)^2+(-5)^2} \\ \text{Distance = }\sqrt[]{1+25} \\ \text{Distance = }\sqrt[]{26}=5.1 \end{gathered}[/tex]
So, the radius of the circle is 5.1
Finally, the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center and r is the radius. So, replacing (h, k) by (1, -3) and r by 5.1, we get that the equation of the circle is:
[tex]\begin{gathered} (x-1)^2+(y-(-3))^2=5.1^2 \\ (x-1)^2+(y+3)^2=26 \end{gathered}[/tex]
