Question

The center of a circle is at (5, - 12) and it has a radius of 16. What is the equation of the circle?

Answer 1

@jim_thompson5910

Answer 2

hint: the general equation of any circle is

(x-h)^2+(y-k)^2=r^2

Answer 3

the center of that circle above is (h,k)

the radius is r

Answer 4

@jim_thompson5910

Answer 5

(h,k) = (5,-12)

so h = 5, k = -12

Answer 6

the radius is 16, so r = 16

Answer 7

plug h = 5, k = -12, r = 16 into (x-h)^2+(y-k)^2=r^2

Answer 8

Do you mind working it out more with me please? @jim_thompson5910

Answer 9

what do you get when you plug those values in?

Answer 10

I got 33 :/

Answer 11

you shouldn't replace x or y

Answer 12

I mean 66

Answer 13

(x-h)^2+(y-k)^2=r^2

(x-5)^2+(y-k)^2=r^2 ... plug in h = 5

(x-5)^2+(y-(-12))^2=r^2 ... plug in k = -12

(x-5)^2+(y-(-12))^2=4^2 ... plug in r = 4

and simplify from here

Answer 14

you won't get a single numeric value because you aren't replacing x or y with values

Answer 15

oh sry, typo, I meant to say on the last line

(x-5)^2+(y-(-12))^2=16^2

since the radius is 16 and not 4

Answer 16

anyways, you have to simplify (x-5)^2+(y-(-12))^2=16^2 to get the answer

Answer 17

help me simplify this because im having a hard time and its not you your correct with everything I just need to see you simplify and fill in the x and y's in the equation

Answer 18

what does y - (-12) simplify to

Answer 19

what # replaces y?

Answer 20

y is left alone

Answer 21

y is just a variable and don't worry about it

Answer 22

y - (-12) turns into ???

Answer 23

I got 12

Answer 24

where did y go?

Answer 25

I put 0 for y

Answer 26

just leave it as it is

Answer 27

y - (-12) simplifies to y + 12

Answer 28

because subtracting a negative is the same as adding a positive

Answer 29

what is 16^2 ?

Answer 30

256?

Answer 31

correct

Answer 32

so my answer would be C?

Answer 33

correct again

Answer 34

Thank You So Much! do you think you can help me with this one?

Answer 35

ok I can help with one more

how far did you get with this one?

Answer 36

I just started it

Answer 37

any ideas on how to answer?

Answer 38

If not, then I recommend finding the center first

Answer 39

ok how do I do that

Answer 40

the center is the midpoint of the segment from (2,0) to (2,-14)

Answer 41

do I count the squares ?

Answer 42

you could, or you can use the midpoint formula

Answer 43

I counted 7 down the (2,0) to (2,-14)

Answer 44

to what point?

Answer 45

2 to 14

Answer 46

you are correct in saying you go 7 units down

Answer 47

since 7 is half of 14

Answer 48

start at (2,0)

travel 7 units down

where do you end up?

Answer 49

14

Answer 50

that doesn't make any sense

Answer 51

you have to end up at an ordered pair or point

Answer 52

(2,-14)?

Answer 53

that's the other endpoint

Answer 54

but I want to know the center of this ellipse