Answer:
22. [tex](x-1)^2+(y+2)^2=74[/tex]
26. [tex]x^2+y^2=81[/tex]
Step-by-step explanation:
The center of a circle is the midpoint of the diameter.
[tex]\textsf{midpoint}=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
(where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the endpoints of the diameter)
The radius of the circle is the distance between the center and an endpoint of the diameter.
[tex]\textsf{radius}=\sqrt{(a-x_1)^2+(b-y_1)^2}[/tex]
(where [tex](a,b)[/tex] is the center of the circle, and [tex](x_1,y_1)[/tex] is an endpoint of the diameter)
The center-radius form of a circle: [tex](x - a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Question 22
[tex]\textsf{Let }(x_1,y_1)=(-4.5)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(6,-9)[/tex]
[tex]\textsf{center}=\left(\dfrac{-4+6}{2},\dfrac{5-9}{2}\right)=(1,-2)[/tex]
[tex]\textsf{radius}=\sqrt{(1+4)^2+(-2-5)^2}=\sqrt{74}[/tex]
⇒ equation of circle: [tex](x-1)^2+(y+2)^2=74[/tex]
Question 26
[tex]\textsf{Let }(x_1,y_1)=(0,9)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(0,-9)[/tex]
[tex]\textsf{center}=\left(\dfrac{0+0}{2},\dfrac{9-9}{2}\right)=(0,0)[/tex]
[tex]\textsf{radius}=\sqrt{(0-0)^2+(0-9)^2}=9[/tex]
⇒ equation of circle: [tex]x^2+y^2=81[/tex]
