Answer:
A. The point (-1,1) is on interior side of the circle.
B. The point (10,0) is on circumference of the circle.
C. The point (4, -8) is on exterior side of the circle.
Step-by-step explanation:
The standard form of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] .... (1)
Where, (h,k) is the center of the circle and r is radius.
The given equation of the circle is
[tex](x-3)^2+y^2=49[/tex] .... (2)
From (1) and (2) we get
[tex]h=3,k=0[/tex]
[tex]r^2=49[/tex]
[tex]r=7[/tex]
The center of the circle is (3,0) and radius is 7 units.
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula the distance between point (-1,1) and center (3,0) is
[tex]D=\sqrt{(3+1)^2+(0-1)^2}=\sqrt{17}\approx 4.1<r[/tex]
The point (-1,1) is on interior side of the circle.
Using distance formula the distance between point (10,0) and center (3,0) is
[tex]D=\sqrt{(3-10)^2+(0-0)^2}=\sqrt{47}=7=r[/tex]
The point (10,0) is on circumference of the circle.
Using distance formula the distance between point (4,-8) and center (3,0) is
[tex]D=\sqrt{(3-4)^2+(0+8)^2}=\sqrt{65}\approx 8.1>r[/tex]
The point (4, -8) is on exterior side of the circle.
