Question

Find thecenter andRadius (1,2) (1,0) write the standard form of the equation

Answer 1

Find the

center and

Radius (1,2) (1,0) write the standard form of the equation

Step 1

by the graph, let's assume the coordinates are of the center and an external point of the circle.

find the radius, use the distance between two points formula

remember

`\begin{gathered} \text{let} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}`

the distance between P1 and P2 is given by:

`d=\sqrt{(y_2-y_1_{})^2+(x_2-x_1_{}_{})^2}`

replace the values

let P1(1,2) and P2(1,0)

`\begin{gathered} d=√((y_2-y_1)^2+(x_2-x_1)^2) \\ d=√((0-2)^2+(1-1)^2) \\ d=√(4) \\ d=2 \end{gathered}`

therefore, the radius is 2

Step 2

the standard form of the equation of a circle is

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where (h,k) is the center of the circle and r is the radius} \end{gathered}`

by the graph, the center is (1,2), so replace

`\begin{gathered} (x-1)^2+(y-2)^2=2^2 \\ (x-1)^2+(y-2)^2=4 \end{gathered}`

and that's all, it would be your answer. I hope it helps you