Answer:
Area of circle = 50.24 units
Option J is correct answer.
Step-by-step explanation:
We need to find the area of a circle with centre (2, 3) that passes through (2,7)
The formula used to find area of circle is:
[tex]Area\: of\: circle=\pi \:r^2[/tex]
We need to find radius.
The radius can be found using the distance between points (2,3) and (2,7)
The The distance formula is: [tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Putting values and finding length
We have: [tex]x_1=2, y_1=3, x_2=2, y_2=7[/tex]
Putting values and finding distance
[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance = \sqrt{(2-2)^2+(7-3)^2}\\Distance = \sqrt{(0)^2+(4)^2}\\Distance = \sqrt{0+16}\\Distance = \sqrt{16}\\Distance = 4[/tex]
So, we found Distance = 4
Therefore, the radius of circle is 4
Now, finding area:
[tex]Area\: of\: circle=\pi \:r^2\\Area\: of\: circle=3.14\times (4) ^2\\Area\: of\: circle=3.14\times 16\\Area\: of\: circle=50.24 \:units[/tex]
So, Area of circle = 50.24 units
Option J is correct answer.
