Question

How do I find the center and the radius of (x – 5)^2 + (y + 2)^2 = 16?

Answer 1

center of \[(x-h)^2+(y-k)^2=r^2\] is \((h,k)\)

Answer 2

and the radius is \(r\)

Answer 3

in your example \(r^2=16\) so \(r\) is easy to find

Answer 4

R would be 8, right?

Answer 5

oh no

Answer 6

Wait I mean 4!

Answer 7

\(8^2=64\) not \(16\)

Answer 8

yes

Answer 9

how about the center, you go that?

Answer 10

Hm,not really..

Answer 11

(h,k) = (5,2)?

Answer 12

\[(x-\color{red}h)^2+(y-\color{blue}k)^2=r^2\] has center \((\color{red}h,\color{blue}k)\)
close but not quite

Answer 13

Oh so (h,k)=(2,5)? Sorry this is a new chapter for me..!

Answer 14

\[(x-5)^2+(y+2)^2=4^2\]
\[(x-5)^2+(y--(-2))^2=4^2\] center is \((5,-2)\)

Answer 15

typo there, too many minus signs
i meant
\[(x-5)^2+(y-(-2))^2=4^2\] center is \((5,-2)\) and radius is \(4\)

Answer 16

you were closer the first time.
the \(h\) i.e. the first coordinate goes with the \(x\) and the \(k\) the second coordinate goes with the \(y\)

Answer 17

Okay, got it. So the center is just an equation?

Answer 18

Thank you so much, by the way! I really appreciate it! c: