Question

A circle is represented by the equation below:

(x + 8)2 + (y − 3)2 = 100

Which statement is true?

The circle is centered at (−8, 3) and has a radius of 20.

The circle is centered at (8, −3) and has a diameter of 20.

The circle is centered at (8, −3) and has a radius of 20.

The circle is centered at (−8, 3) and has a diameter of 20.

Answer 1

\(\large (x-h)^2+(y-k)^2=r^2 \), is the equation of a circle whose RADIUS is r, and center (h, k)

according to the equation you gave,
what's your radius?
what's your center?

Answer 2

I think that the answer is C because of one pair of (x + 8)2 being positive and (y − 3)2 being negative. @dpaInc

Answer 3

no.... C says the radius is 20... it's not 20

Answer 4

so would it be the diameter is 20 and the radius is 10? therefore making it B?

Answer 5

the diameter is 20....
look at your equation carefully.... what's the center?

Answer 6

I see the +8 and -3 so i thought it was those... do they switch because of the squaring?

Answer 7

no, not because of the squaring... the equation have to written in standard form (with minus signs):

\(\large (x+8)^2+(y-3)^2=100 \)
\(\large (x--8)^2+(y-3)^2=10^2 \)
\(\large (x-(\color{red} {-8}))^2+(y-(\color{red}3))^2=(\color{red}{10})^2 \)

so that's how you get the center...

Answer 8

So the center is (8,-3) correct? with a diameter of 20?

Answer 9

it's in RED... center is (-8, 3) with a diameter of 20

Answer 10

oh. i saw the double negative so i thought it became a positive

Answer 11

just remember, if it's written with a plus sign, you need to write it with a minus like:

\(\large (x+8)^2=(x--8)^2 \) so h=-8 in this case

Answer 12

ok thank you :) i may have a few more questions and you explain them very well can i tag you in them when i get to them?

Answer 13

yep... no problem...

Answer 14

thx