A. is inside of the circle.
B. is on the circle
C. is outside of the circle.
This is because you can find the center of the circle using the base formula for a circle. (x - h)^2 + (y - k)^2 = r^2, with the center being (h, k). Using this fact, we know the center to be (3,0).
We can also use that formula to find the radius. Since the radius squared is equal to 49, we can find the radius.
r^2 - 49
r = 7
Now we can see how far each points are away from the center to see if they are less than, greater than or equal to 7. This will tell us if they are close enough.
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.
If a circle O has radius of r units lengcircle th and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:
(x-h)^2 + (y-k)^2 = r^2 .....(1)
The given equation of the is
[tex](x - 3)^2 + y^2 = 49[/tex] .... (2)
From (1) and (2) we get,
h =3, k = 0
r = 7
Thus, the center of the circle is (3,0) and radius is 7 units.
Distance formula:
D = √[(x-p)² + (y-q)²]
Using distance formula the distance between point (-1,1) and center (3,0).
D = √[(3 + 1)² + (0 -1)²]
D = 7.1
The point (-1,1) is on interior side of the circle.
Using distance formula the distance between point (10,0) and center (3,0) ;
D = √[(3- 10)² + (0 - 0)²]
D = 7 = r
The point (10,0) is on circumference of the circle.
Using distance formula the distance between point (4,-8) and center (3,0);
D = √[(3-4 )² + (0 + 8)²]
D = 8.1
Hence, The point (4, -8) is on exterior side of the circle.
Learn more about equation of a circle here:
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