cutiecomittee123
  • cutiecomittee123
how do find the vertex and foci of this hyperbola (x-2)^2/36 - (y+1)^2/64 =1
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
misty1212
  • misty1212
HI!!!
misty1212
  • misty1212
standard form is \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] you get the center with your eyeballs right?
misty1212
  • misty1212
this is where you say "yes i see it" or "no i have no clue"

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

cutiecomittee123
  • cutiecomittee123
yes:)
misty1212
  • misty1212
ok what is the center?
cutiecomittee123
  • cutiecomittee123
(2,-1)
misty1212
  • misty1212
ok good now we need to know one other thing what does it look like left or right?|dw:1433186027332:dw|
cutiecomittee123
  • cutiecomittee123
second, its horizontal
misty1212
  • misty1212
hmmm no
misty1212
  • misty1212
the \(x\) term comes first, vertical
misty1212
  • misty1212
now that we (presumably) have these two facts, the orientation and the center, the rest is easy
cutiecomittee123
  • cutiecomittee123
oh gotcha
misty1212
  • misty1212
the center is \((2,-1)\) and it is vertical that means the vertices are to the LEFT and RIGHT of the center (that is why we need the orientation first)
misty1212
  • misty1212
if it was horizontal they would be up and down
cutiecomittee123
  • cutiecomittee123
okay makes sense.
misty1212
  • misty1212
you have \[\frac{(x-2)^2}{36}-\frac{(y+1)^2}{64}=1\] which looks like \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] what is \(a\)?
cutiecomittee123
  • cutiecomittee123
a=6
misty1212
  • misty1212
right so how easy is this? the vertices are 6 units to the right and left of \((2,-1)\)
misty1212
  • misty1212
got that ?
cutiecomittee123
  • cutiecomittee123
okay so (-8, -1) and (5, -1)
misty1212
  • misty1212
hmm no to the second one
misty1212
  • misty1212
oh no no to both of them
misty1212
  • misty1212
what is 6 units to the left of \((2,-1)\)?
misty1212
  • misty1212
or is simple english , what is \(2-6\) and \(2+6\)?
cutiecomittee123
  • cutiecomittee123
oh lol. (-4,-1) and (8,-1)
misty1212
  • misty1212
whew!
cutiecomittee123
  • cutiecomittee123
better?
misty1212
  • misty1212
ok that takes care of the vertices now for the foci
misty1212
  • misty1212
much yes
cutiecomittee123
  • cutiecomittee123
alright so how do we find the foci?
misty1212
  • misty1212
we need one number number , namely \(c\) and we find it like pythagoras \[a^2+b^2=c^2\]
misty1212
  • misty1212
you got \(a^2=36,b^2=64\) what is \(c\)?
cutiecomittee123
  • cutiecomittee123
so 36+64=100
misty1212
  • misty1212
right and so \(c^2=100\) making \(c=?\)
cutiecomittee123
  • cutiecomittee123
c=10
cutiecomittee123
  • cutiecomittee123
well + or - 10
misty1212
  • misty1212
just plus
misty1212
  • misty1212
so now (don't mess this up!) what is ten units to the right and left of \((2,-1)\)?
cutiecomittee123
  • cutiecomittee123
(12,-1) and (8,-1)
misty1212
  • misty1212
lol
misty1212
  • misty1212
i know what you meant (i hope)
misty1212
  • misty1212
\[(12,-1)\] is ten units the the right, \[(\color{red}-8,1)\] is ten units to the left
cutiecomittee123
  • cutiecomittee123
yeah :)
misty1212
  • misty1212
ok that is it
cutiecomittee123
  • cutiecomittee123
thank you :)
misty1212
  • misty1212
it is really not that hard people here don't like it and math teachers make it seem way harder than it is you see we really only needed two things the center and the orientation
cutiecomittee123
  • cutiecomittee123
yeah it seems simple
misty1212
  • misty1212
\[\color\magenta\heartsuit\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.