Question

Find the center and radius of the circle. Write the standard form of theequation.(2,5)(5,5)

Answer 1

If (2.5) and (5,5) are the two end points of the circle, then the center of the circle is the midpoint

To find the midpoint, we will use the formula

`(x_m,y_m)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

x₁ = 2 y₁=5

x₂=5 y₂=5

Substitute into the formula and evaluate

`(x_m,y_m)=((2+5)/(2),(5+5)/(2))`
`=((7)/(2),(10)/(2))`
`=((7)/(2),5)`

Hence, the center of the circle is (7/2 , 5)

To find the radius, we can simply find the distance between the end points and divide by 2

Using the distance formula,

`|d|=\sqrt[]{(5-2)^2+(5-5)^2}`
`=\sqrt[]{3^2}=3`

Hence, the radius is 3

The general formula for the equation of a circle centered (h,k) and radius r is given by

`(x-h)^2+(y-k)^2=r^2`

substitute the values into the formula

`(x-(7)/(2))^2+(y-5)^2=3^2`

Therefore, the equation of the circle is:

`(x-(7)/(2))^2+(y-5)^2=9`