Consider a circle with center (2,-3) that passes through the point (5,4). What is the equation of the described circle?
A) (x - 2)^2 + (y + 3)^2 = 58
B) (x - 2)^2 + (y + 3)^2 = 68
C) (x + 2)^2 + (y - 3)^2 = 58
D) (x + 2)^2 + (y - 3)^2 = 68

If the circle passes through the point (6,5), what is the equation of the new circle with the same center?
A) (x + 2)^2 + (y - 3)^2 = 80
B) (x + 2)^2 + (y - 3)^2 = 90
C) (x - 2)^2 + (y + 3)^2 = 80
D) (x - 2)^2 + (y + 3)^2 = 90

Part A: A. Part B: C

Step-by-step explanation:

Substitute the number into the equation of circle: (x-h)^2 + (y-k)^2=r^2

h and k are 2, -3 so you will need to change their signs.

The final thing you will do is to find the distance of center to point. Using distance formula and you will able to find the radius. Square your radius then the result will be there

good luck!

cutie~

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}