Verify if these points lie on the interior, exterior, or on the circle: (1,2), (2,0), and (3,2). Circle Equation is: open parentheses x plus 1 close parentheses squared plus y squared equals 9

(1,2): Interior

(2,0): On

(3,2): Exterior

Step-by-step explanation:

The circle equation is (x+1)^2 + y^2 = 9

To know if a point is inside, outside or on a circle, we first calculate the distance from this point to the center of the circle, using this equation:

d = sqrt(dx^2 + dy^2), where

d is the distance between the points,

dx is the difference in x axis between the points,

dy is the difference in y axis between the points.

The circle generic equation is (x−a)2 + (y−b)2 = r^2, where the point (a,b) is the circle's center.

So, looking at our circle equation, we know that the center is at (-1,0), and its radius is 3.

Now, we calculate the distance from our 3 points to the center of the circle:

point (1,2): dx = (1-(-1)) = 2, dy = 2-0 = 2, d = sqrt(2^2 + 2^2) = sqrt(8) =  2.8284

As this distance is lesser than the circle radius, this point is INTERIOR to the circle

point (2,0): dx = (2-(-1)) = 3, dy = 0-0 = 0, d = sqrt(3^2 + 0^2) = sqrt(9) =  3

As this distance is equal the circle radius, this point is ON the circle

point (3,2): dx = (3-(-1)) = 4, dy = 2-0 = 2, d = sqrt(4^2 + 2^2) = sqrt(20) = 4.4721

As this distance is greater than the circle radius, this point is EXTERIOR to the circle.

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

a - base

b - exponent

so,