Given the circle with the equation (x - 3)2 + y2 = 49, determine the location of each point with respect to the graph of the circle. in your final answer, state whether each point is on the interior, exterior, or circumference of the circle. include your calculations as proof of each point’s location.
a. (-1, 1)
b. (10, 0)
c. (4, -8)

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

            .... (1)

Where, (h,k) is the center of the circle and r is radius.

The given equation of the circle is

                 .... (2)

From (1) and (2) we get

The center of the circle is (3,0) and radius is 7 units.

Distance formula:

Using distance formula the distance between point (-1,1) and center (3,0) is

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

The point (10,0) is on circumference of the circle.

Using distance formula the distance between point (4,-8) and center (3,0) is

The point (4, -8) is on exterior side of the circle.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."