Given the circle with the equation (x + 1)2 + y2 = 36, 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. (-1, 6) C. (4, -8)

First, we need to plug these points into the equation given to find our inequality. If the answer is lower then the number the equation equals (36) it's on the interior, if it's equal, it's on the circumference, and if it's greater its on the exterior.

A. (-1 + 1)^2 + 1^2 =? 36

0^2 + 1 =? 36

0 + 1 =? 36

We get the value

1 < 36

This point is on the interior of the circle

B. (-1 + 1)^2 + 6^2 =? 36

0^2 + 36 =?36

0 + 36 =? 36

we get the value

36 = 36

This point is on the circumference of the circle

C. (4 + 1)^2 + -8^2 =? 36

5^2 + 64 =? 36

25 + 64 =? 36

we get the value

89 > 36

this point is on the exterior of the circle.

jainveenamrata jainveenamrata · Answer 2 · 2022-08-18T15:16:34+02:00

The circle is passing through (-1, 6). Then the correct option is B.

What is the equation of a circle?

Let r be the radius of the circle and the location of the center of the circle be (h, k).

Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

The equation is given below.

(x + 1)² + y² = 36

(x + 1)² + y² = 6²

Then the center of the circle will be (-1, 0).

The location of each point with respect to the graph of the circle.

From the graph, the circle is passing through (-1, 6).

The point (-1, 6) will satisfy the equation.

(-1 + 1)² + 6² = 36

36 = 36

Then the correct option is B.

The graph of the circle is given below.

More about the equation of circle link is given below.

https://brainly.com/question/10618691

#SPJ2