Question

Find the center radius form for each circle having the given endpoints of a diameter.

22. (-4,5) and (6,-9)

26. ( 0,9) and (0,-9)

Answer 1

22.
`(x-1)^2+(y+2)^2=74`

26.
`x^2+y^2=81`

Explanation:

The center of a circle is the midpoint of the diameter.

`\textsf{midpoint}=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

(where
`(x_1,y_1)` and
`(x_2,y_2)` are the endpoints of the diameter)

The radius of the circle is the distance between the center and an endpoint of the diameter.

`\textsf{radius}=√((a-x_1)^2+(b-y_1)^2)`

(where
`(a,b)` is the center of the circle, and
`(x_1,y_1)` is an endpoint of the diameter)

The center-radius form of a circle:
`(x - a)^2+(y-b)^2=r^2`

(where (a, b) is the center and r is the radius)

Question 22

`\textsf{Let }(x_1,y_1)=(-4.5)`

`\textsf{Let }(x_2,y_2)=(6,-9)`

`\textsf{center}=\left((-4+6)/(2),(5-9)/(2)\right)=(1,-2)`

`\textsf{radius}=√((1+4)^2+(-2-5)^2)=√(74)`

⇒ equation of circle:
`(x-1)^2+(y+2)^2=74`

Question 26

`\textsf{Let }(x_1,y_1)=(0,9)`

`\textsf{Let }(x_2,y_2)=(0,-9)`

`\textsf{center}=\left((0+0)/(2),(9-9)/(2)\right)=(0,0)`

`\textsf{radius}=√((0-0)^2+(0-9)^2)=9`

⇒ equation of circle:
`x^2+y^2=81`