Question

Given the circle with the equation x2 + y2 = 5, 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. (-2, 1)
C. (4, -8)

Answer 1

The circle's equation tells us that it is centered at the origin and that the radius is the square root of 5, which in numbers is 2.23 rounded.  That means that any points within that radius are inside the circle and any points outside that radius are outside the circle, which tells us our answers to A and C.  A is well within the radius at (-1,1) and C is way outside at (4, -8). Now let's look at B.  We have our equation and we also have a radius squared of 5, so let's fit the x and the y values of the point (-2, 1) into that equation and see if what we get is equal to the radius squared that they give us.
If $x^{2} + y^{2} =5$
then $-2^{2} + 1^{2}$ should = 5.  It does, so that coordinate for B lies directly on the circle.

Answer 2

Answer:

Step-by-step explanation:

First, we need to plug each point into the equation separately to find their inequality. If the answer is greater than the number equal to the equation (5) the point is on the exterior of the circle, if the answer is equal, it's on the circumference, and if the answer is lesser than, it's on the interior.

A. (-1)^2 + (1)^2 =? 5

1 + 1 =? 5

we get the value

2 < 5

The point is on the interior of the circle

B. (-2)^2 + (1)^2 =? 5

4 + 1 =? 5

we get the value

5 = 5

the point is on the circumference of the circle

C. (4)^2 + (-8)^2 =? 5

16 + 64 =? 5

we get the value

80 > 5

the point is on the exterior of the circle