Question

Find the center and radius. x^2 + y^2 +20x -2y -92=0

Answer 1

you need to apply completing the square here, for both x and y, then you can establish the normal equation of a circle.

Answer 2

\[x^2 + 20x + x^2 - 2y = 92\]

\[x^2 + 20x + (10)^2 + y^2 - 2y + (1)^2 = 92 + (10)^2 + (1)^2\]

\[\large (x + 10)^2 + (y - 1)^2 = (\sqrt{193})^2\]

Here radius is \(\sqrt{193} \approx 13.9\)

Center is : \((-10, 1)\)

Answer 3

why is there a sq root on top of the 193? @waterineyes

Answer 4

@karatechopper

Answer 5

@GOODMAN

Answer 6

hey can u plz explain to me why there is a sq rt over the 193 and the sqaured

Answer 7

Because you need to find the radius. And the radius is the diameter squared. So 193 was the diameter, but we need the radius. So @waterineyes squared it..

Answer 8

ok

Answer 9

@Calcmathlete can you plz explain this same question again without bothering about water in eye's posts

Answer 10

@saifoo.khan can u plz explain this question

Answer 11

Sorry, i never studied eclipse. :/

Answer 12

huh? how but ur so smart?

Answer 13

calc plz help me

Answer 14

lol @saifoo.khan This is a circle XD Well, I guess a circle is a type of ellipse

Answer 15

Alright. Hold on.

Answer 16

Do you understand what water above did? She completed the square. Are you familiar with it?

Answer 17

yep with completing the square

Answer 18

lol. Yup! similar things..

Answer 19

Do yuo understand how it works though?

Answer 20

nope I think she messed up somewhere

Answer 21

Ok. Let's see...
\[x^2 + y^2 + 20x - 2y - 92 = 0\]\[x^2 + y^2 + 20x - 2y = 92\]\[x^2 + 20x + y^2 - 2y = 92\]\[x^2 + 20x + 100 + y^2 - 2y + 1 = 92 + 100 + 1\]\[(x + 10)^2 + (y - 1)^2 = 193\]THis is the form that you need it in. The form for a circle is \[(x - h)^2 + (y - k)^2 = r^2\]Do yuo see the resemblance?

Answer 22

The center of a circle is (-h, -k) and the radius is 4. Do you know how to get them now?

Answer 23

I mean the radius is r.

Answer 24

Are you following???

Answer 25

alright sry, my mom called me

Answer 26

sryy to keep you waiting

Answer 27

Do you get what to do from there?

Answer 28

yes I already go the answer

Answer 29

thx though

Answer 30

np :)