toxicsugar22
  • toxicsugar22
give the exact coordinates of any four points on the hyperbola (y+2)^2/6-(x+2)^2/10=1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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toxicsugar22
  • toxicsugar22
hi ccan u help me
anonymous
  • 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 \((-2,\sqrt6-2)\).
toxicsugar22
  • toxicsugar22
how about another point

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toxicsugar22
  • toxicsugar22
how abut another point for x
anonymous
  • anonymous
Show me what you can do with \(x=8\).
toxicsugar22
  • toxicsugar22
(y+2)^2/6-(8+2)^2/10=1
toxicsugar22
  • toxicsugar22
and then show me by step by step
anonymous
  • 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 :)
anonymous
  • anonymous
*Take -10 to the other side with a positive sign*
toxicsugar22
  • toxicsugar22
so (y+2)^2/6=11
toxicsugar22
  • toxicsugar22
now what do i do
anonymous
  • anonymous
I wrote all steps you need in my last comment; now multiply both sides by 6.
toxicsugar22
  • toxicsugar22
s0 (y+2)^2/36=66
toxicsugar22
  • toxicsugar22
is that rigtht so far
anonymous
  • anonymous
Not quite. It should be, after multiplying by 6: \((y+2)^2=66\).
toxicsugar22
  • toxicsugar22
ok
toxicsugar22
  • toxicsugar22
so now it will be (y+2)^2=8.1240
anonymous
  • anonymous
Yeah, but this is not "exact". You should write it as \((y+2)^2=\sqrt{66}\).
toxicsugar22
  • toxicsugar22
so now what
anonymous
  • anonymous
Sorry I meant \(y+2=\sqrt{66}\). Now take 2 to the other side with a minus sign, and you're done :D
toxicsugar22
  • toxicsugar22
y=sqrt66-2
anonymous
  • anonymous
Yep.
toxicsugar22
  • toxicsugar22
yeah
toxicsugar22
  • toxicsugar22
ok and how about lets try 3 for x
toxicsugar22
  • toxicsugar22
can uwe do an easier number
anonymous
  • anonymous
Go for i!! I am sure you can do it. You will get \(y=\sqrt{21}-2\). I have to go now :(
anonymous
  • anonymous
\(3\) is good.

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