Question

give the exact coordinates of any four points on the hyperbola

(y+2)^2/6-(x+2)^2/10=1

Answer 1

hi ccan u help me

Answer 2

That's pretty easy. Just choose any 4 points for x, and find the corresponding values of y. I'll do one for you. Let's take x=-2, plug in the equation and solve for x to get: \((y+2)^2/6-0=1\), which implies that \((y+2)^2=6\). Taking the square root of both sides gives \(y+2=\sqrt{6}\), and therefore \(y=\sqrt6-2 \). So, a point on the given hyperbola is \((-2,\sqrt6-2)\).

Answer 3

how about another point

Answer 4

how abut another point for x

Answer 5

Show me what you can do with \(x=8\).

Answer 6

(y+2)^2/6-(8+2)^2/10=1

Answer 7

and then show me by step by step

Answer 8

\[{(y+2)^2 \over 6}-{(8+2)^2 \over 10}=1 \implies {(y+2)^2 \over 6}-{100 \over 10}=1 \implies {(y+2)^2 \over 6}-10=1\]
Now take 10 to the other side and then multiply both sides by 6. After that, take the square root and then subtract 2 from both sides.
Please TRY :)

Answer 9

*Take -10 to the other side with a positive sign*

Answer 10

so (y+2)^2/6=11

Answer 11

now what do i do

Answer 12

I wrote all steps you need in my last comment; now multiply both sides by 6.

Answer 13

s0 (y+2)^2/36=66

Answer 14

is that rigtht so far

Answer 15

Not quite. It should be, after multiplying by 6: \((y+2)^2=66\).

Answer 16

ok

Answer 17

so now it will be (y+2)^2=8.1240

Answer 18

Yeah, but this is not "exact". You should write it as \((y+2)^2=\sqrt{66}\).

Answer 19

so now what

Answer 20

Sorry I meant \(y+2=\sqrt{66}\). Now take 2 to the other side with a minus sign, and you're done :D

Answer 21

y=sqrt66-2

Answer 22

Yep.

Answer 23

yeah

Answer 24

ok and how about lets try 3 for x

Answer 25

can uwe do an easier number

Answer 26

Go for i!! I am sure you can do it. You will get \(y=\sqrt{21}-2\). I have to go now :(

Answer 27

\(3\) is good.