Question

The point (2,n) lies on the circle whose equation is (x-3)^2+(y+2)^2=26.Find the value of n.

Answer 1

you can plug in x= 2, and y =n in the circle's equation.
and solve for n :)

Answer 2

If the x is 2, you can easily plug it in the equation and solve for it.

Answer 3

Oh, yea what hartnn said :P

Answer 4

note: you'll get 2 values of n

Answer 5

So it would be (2-3)^2+(y+2)^2=26?

Answer 6

yes

Answer 7

Okay,then do I just do the 2-3^2 and get -1 then do -1+(y+2)^2=26?

Answer 8

brackets are important :)
\((2-3) = -1 \\ (2-3)^2 = (-1)^2 = +1\)

Answer 9

\((-1)^2 = (-1)\times(-1) = 1\)

Also, without brackets,
2-3^2 = 2-9 = -7 which is totally incorrect :P

Answer 10

\[+1+n^2+4n+4=26\]
\[n^2+4n=21\]
\[n^2+4n-21 =0\]

Answer 11

doing square root on both sides would be easier :)

Answer 12

@August899 use delta to find n that's simple

Answer 13

So I do -1+(y+2)^2=26,What do I do afterwards?

Answer 14

its not -1


\((2-3)^2 + (n+2)^2 = 26 \\ (-1)^2 + (n+2)^2 = 26 \\1 + (n+2)^2 = 26\)
you get this?

Answer 15

Oh okay. Yes I get it now.

Answer 16

now subtract 1 from both sides

Answer 17

Okay.So now it is (n+2)^2=25

Answer 18

yes
take square root on both sides

Answer 19

I square root the (n+2)^2 correct?

Answer 20

and that equals 5 because the square root of 25 is 5

Answer 21

with your method, dinamix,
b^2 -4ac = 16- 4(1)(-21) = 16+4*21 = ...

yes August.

Answer 22

yup sorry its +17

Answer 23

@August899
\(a^2 = b^2 \implies a = \pm b\)

Answer 24

\((n+2)^2 =5^2 \implies n+2 = \pm 5\)

Answer 25

How do I do the square root of (n+2)^2? Do I do 2^2 which 4 and do the square root which is 2 and do 2=25 and divide by 2?

Answer 26

\(\Large \sqrt{(anything)^2 } = anything \\ \Large \sqrt{(n+2)^2} = n+2\)

Answer 27

Ohh okay.Then I subtract 2 from both sides?

Answer 28

\[\sqrt{(n+2)^2}=|n+2|\]

Answer 29

yes yes

Answer 30

Okay I got n=3

Answer 31

Thank you sooo much for the help!

Answer 32

\(\color{blue}{\text{Originally Posted by}}\) @Zarkon
\[\sqrt{(n+2)^2}=|n+2|\]
\(\color{blue}{\text{End of Quote}}\)

\(|n+2| = 5 \\n+2 = \pm 5 \)

Answer 33

you will have one more value of n

Answer 34

n +2 = 5 ... n = 3

n+2 = -5 ... n = ...?

Answer 35

7?

Answer 36

n +2 = -5
subtract 2 from both sides

Answer 37

-7

Answer 38

\(\checkmark \)

Answer 39

so the 2 values of n are 3, -7 :)

Answer 40

Thank you! I understand it now.

Answer 41

welcome ^_^