## toxicsugar22 5 years ago give the exact coordinates of any four points on the hyperbola (y+2)^2/6-(x+2)^2/10=1

1. toxicsugar22

hi ccan u help me

2. anonymous

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 $$(-2,\sqrt6-2)$$.

3. toxicsugar22

how about another point

4. toxicsugar22

how abut another point for x

5. anonymous

Show me what you can do with $$x=8$$.

6. toxicsugar22

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

7. toxicsugar22

and then show me by step by step

8. anonymous

${(y+2)^2 \over 6}-{(8+2)^2 \over 10}=1 \implies {(y+2)^2 \over 6}-{100 \over 10}=1 \implies {(y+2)^2 \over 6}-10=1$ 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 :)

9. anonymous

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

10. toxicsugar22

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

11. toxicsugar22

now what do i do

12. anonymous

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

13. toxicsugar22

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

14. toxicsugar22

is that rigtht so far

15. anonymous

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

16. toxicsugar22

ok

17. toxicsugar22

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

18. anonymous

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

19. toxicsugar22

so now what

20. anonymous

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

21. toxicsugar22

y=sqrt66-2

22. anonymous

Yep.

23. toxicsugar22

yeah

24. toxicsugar22

ok and how about lets try 3 for x

25. toxicsugar22

can uwe do an easier number

26. anonymous

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

27. anonymous

$$3$$ is good.