Answer:
area of circle in terms of π is ![\mathbf{Area=6.25\:\pi }](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%3D6.25%5C%3A%5Cpi%20%7D)
Step-by-step explanation:
The endpoints of a diameter of a circle are A(3,2) and B(6,6). Find the area of the circle in terms of π.
The formula used to find area of circle is: ![Area = \pi r^2](https://tex.z-dn.net/?f=Area%20%3D%20%5Cpi%20r%5E2)
We need to find radius of circle. For finding radius we will first find diameter of circle using distance formula.
Finding distance between points A(3,2) and B(6,6) using distance formula.
![Distance\:Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=Distance%5C%3AFormula%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
We have ![x_1=3, y_1=2, x_2=6, y_2=6](https://tex.z-dn.net/?f=x_1%3D3%2C%20y_1%3D2%2C%20x_2%3D6%2C%20y_2%3D6)
Putting values and finding distance
![Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-3)^2+(6-2)^2}\\Distance=\sqrt{(3)^2+(4)^2}\\Distance=\sqrt{9+16}\\Distance=\sqrt{25}\\Distance=5](https://tex.z-dn.net/?f=Distance%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%5C%5CDistance%3D%5Csqrt%7B%286-3%29%5E2%2B%286-2%29%5E2%7D%5C%5CDistance%3D%5Csqrt%7B%283%29%5E2%2B%284%29%5E2%7D%5C%5CDistance%3D%5Csqrt%7B9%2B16%7D%5C%5CDistance%3D%5Csqrt%7B25%7D%5C%5CDistance%3D5)
So, distance is 5, we can say that diameter of circle = 5
The formula used to find area of circle is: ![Area = \pi r^2](https://tex.z-dn.net/?f=Area%20%3D%20%5Cpi%20r%5E2)
We need radius, so we know that r = d/2 so, radius = 5/2 = 2.5
Now finding area in terms of π
![Area = \pi r^2\\Area=(2.5)^2\pi \\Area=6.25\:\pi](https://tex.z-dn.net/?f=Area%20%3D%20%5Cpi%20r%5E2%5C%5CArea%3D%282.5%29%5E2%5Cpi%20%5C%5CArea%3D6.25%5C%3A%5Cpi)
So, area of circle in terms of π is ![\mathbf{Area=6.25\:\pi }](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%3D6.25%5C%3A%5Cpi%20%7D)