Equations of circles: which points lie inside the circle?

[george22]

A graph contains the point (1, -2) and a radius of 3. Which of the following points lie inside the circle?

(-1, 2)
(3, 0)
(0, -5)
(1, 3)

* the question does not tell me if any of the points are the center so I am having difficulty using the formula.

 

[pka]

Which of the given points is 3 units from (1,-2)?

 

[jacket81]

Wouldn't it mean that the points would have to satisfy equation (x-1)^2 + (y+2)^2 <=9 ?
So,which of the points satisfy that equation?

 

[pka]

Wouldn't it mean that the points would have to satisfy equation (x-1)^2 + (y+2)^2 <=9 ? So,which of the points satisfy that equation?

Well that may be what the questions means.
If so, then the word interior should have been used.
To say that a point is in as set means element of the set.

 

[soroban]

Re: Equations of circles: which points lie inside the circle

Hello, George!

Can you provide the original wording of the problem?
As written, it makes no sense.

22] A graph contains the point (1, -2)

We're already in trouble!
A graph of what? . . . a line? a parabola? a Folium of Descartes?

and a radius of 3

This graph has a radius?
Only a circle has a radius . . . Couldn't they have called it a circle?

Which of the following points lie inside the circle?
. . (-1,2), (3,0), (0,-5), (1,3)

So now they refer to the circle.
Like we know what they're talking about . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The only way the problem makes any sense
\(\displaystyle \;\;\)is if the given point (1,-2) is the center of the circle
\(\displaystyle \;\;\)which should have been stated at the beginning.

For points inside the circle, we have: \(\displaystyle \,(x\,-\,1)^2\,+\,(y\,+\,2)^2\;\)<\(\displaystyle \;9\)

Now test the points to see which one satisfies the inequality.

 

[jacket81]

Sorry, for some reason i assumed (1,-2) was center.
So, if its not, i was entirely wrong.