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

A) (-1,1) -----> The ordered pair is on the interior of the circle

B) (-2,1) -----> The ordered pair is on the circumference of the circle

C) (4,-8) -----> The ordered pair is on the exterior of the circle

Explanation:

we know that

In this problem

1) If a ordered pair satisfy the equation
`x^(2) +y^(2)=5`

then

The ordered pair is on the circumference of the circle

2)If a ordered pair satisfy the inequality
`x^(2) +y^(2)>5`

then

The ordered pair is on the exterior of the circle

3)If a ordered pair satisfy the inequality
`x^(2) +y^(2)< 5`

then

The ordered pair is on the interior of the circle

Verify each case

case A) (-1,1)

For x=-1, y=1

`-1^(2) +1^(2)=2`

so

`x^(2) +y^(2)< 5`

therefore

A) (-1,1) -----> The ordered pair is on the interior of the circle

case B) (-2,1)

For x=-2, y=1

`-2^(2) +1^(2)=5`

so

`x^(2) +y^(2)= 5`

therefore

B) (-2,1) -----> The ordered pair is on the circumference of the circle

case C) (4,-8)

For x=4, y=-8

`4^(2) + (-8)^(2)=80`

so

`x^(2) +y^(2)> 5`

therefore

C) (4,-8) -----> The ordered pair is on the exterior of the circle