Question

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)

Answer 1

This may not help but the first step is to distribute the 2 to the (x - 3) Which would get you to 2x - 3 + y2= 49 Then you will want to subtract 3 from 49 which gives you 46. Now you have 2x+ y2= 49 Now you need you have the standard equation  ax+by=c 

Answer 2

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.

Explanation:

The standard form of the circle is

`(x-h)^2+(y-k)^2=r^2` .... (1)

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

The given equation of the circle is

`(x-3)^2+y^2=49` .... (2)

From (1) and (2) we get

`h=3,k=0`

`r^2=49`

`r=7`

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

Distance formula:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

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

`D=√((3+1)^2+(0-1)^2)=√(17)\approx 4.1<r`

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

`D=√((3-10)^2+(0-0)^2)=√(47)=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) is

`D=√((3-4)^2+(0+8)^2)=√(65)\approx 8.1>r`

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