Question

A circle with center C (4,-2) passes through the point A (1 3). Does the point B (8-2) lie inside the circle?

Answer 1

The correct answer option is A. point B lies inside the circle since CA =
`√(34)` and CB = 4

Explanation:

We are given a circle with the point C (4,-2) as its center which passes through the point A (1, 3) and we are to figure out if the point B (8, -2) lies inside or outside the circle.

We can find this by using the distance formula:

Distance between C and A =
`√((4-1)^2+(-2-3)^2) =  √(34)`

Distance between C and B =
`√((4-8)^2+(-2-(-2)^2) =  √(16) =4`

Therefore, the point B lies inside the circle since CA =
`√(34)` and CB = 4.

Answer 2

Given that a circle with center C (4,-2) passes through the point A (1 3). Now w have to find if the point B (8-2) lie inside the circle or not.

To find that we just need to check if the value of line segment BC is less than AC or not.

to find those distances we can use distance formula which is given by:

`d=√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

where d is distance between points (x1,y1) and (x2,y2)

So using that formula we get:

`CA=√((4-1)^2+(-2-3)^2)`

`CA=√((3)^2+(-5)^2)`

`CA=√(9+25)`

`CA=√(34)`

similarly find CB

`CB=√((4-8)^2+(-2--2)^2)`

`CB=√((-4)^2+(0)^2)`

`CB=√(16+0)`

CB=4

Hence choice A is correct.