Question

The equation of a circle is (x + 7)2 + (y + 2)2 = 49. Determine the length of the diameter.

Answer 1

formula for a circle with radius \(r\) and center \((h,k)\) is
\[(x-h)^2+(y-k)^2 = r^2\]formula for a diameter \(d\) given a radius \(r\) is \[d = 2r\]

Answer 2

i got 49 is that right? @whpalmer4

Answer 3

@whpalmer4 the choices are
7

9

49

14

Answer 4

Let's take baby steps. Using my formula, what do you find for the center of the circle?

Answer 5

what would i plug into the formula?

Answer 6

\[(x-h)^2 + (y-k)^2 = r^2\]\[(x+7)^2+(y+2)^2 = 49\]

what are the values of \(h,k,r\) that make those two equations equal?

Answer 7

7, 2, and 49

Answer 8

I'm sorry, that's 3 strikes...try again?

Answer 9

??? im so confused omg

Answer 10

Hint: do you think \((x-7) = (x+7)\)?

Answer 11

no

Answer 12

Your answer suggests otherwise!

Answer 13

-7, -2, and 49?

Answer 14

now you have 2 of the 3 correct :-)

does 49*49 = 49?

Answer 15

2408 is what 49*49=

Answer 16

-7, -2, and 2408

Answer 17

no, 49*49 = 2401 , and that's not 49. for the two equations to be equal, \(r^2 = 49\), right?

Answer 18

yeah

Answer 19

okay, so if \[r^2=49\]what does \(r=\)

Answer 20

r=7

Answer 21

good. if \(r=7\), what does \(d=\)

Answer 22

d=14?

Answer 23

as an old math teacher of mine used to say when someone answered with uncertainty in their voice, "is that an answer, or a prayer?" :-)

Answer 24

d=14!

Answer 25

there shouldn't be any need for uncertainty as to the value of \(d = 2r\) if you know that \(r = 7\)

that's better!

Answer 26

thank you so much! can you help with one more? I'll ask a new question :)

Answer 27

so, this sort of pattern-matching is a very useful and important thing to grasp. let's do another one as practice:

\[(x+1)^2 + (y-3)^2 = 25\]

what is the center of that circle, and what is the radius? again, the formula for the circle with center at \((h,k)\) and radius \(r\) is:
\[(x-h)^2 + (y-k)^2 = r^2\]

Answer 28

ok so the center is -1, the radius is 3

Answer 29

:-(

isn't the center a point with 2 coordinates? and does 3*3 = 25?

Answer 30

ugh im so confused again! im supposed to multiply?

Answer 31

let's go through it again:

\[(x+1) = (x-h)\]\[x+1 = x-h\]subtract \(x\) from both sides
\[+1 = -h\]\[h = -1\]

\[(y-3) = (y-k)\]\[y-3=y-k\]\[-3=-k\]\[k=3\]
so the center is at \((h,k) = (-1,3)\)

Answer 32

looking at the right side of the equation,
\[r^2 = 25\]\[r =\]

Answer 33

yeah ok i get that. i don't know why you asked if 3*3 is 25 though??

Answer 34

r=5

Answer 35

you said the radius was 3! I'm saying you couldn't possibly have checked your answer for reasonableness, unless you think that 3*3 = 25, because the value of the radius ^2 has to equal 25

Answer 36

oh ok

Answer 37

you had another problem?

Answer 38

yeah i"ll ask it right now. it's a question from a practice test.