Question

HELP!!!!!!!!!!!!





Write the general form of the equation which matches the graph below. In complete sentences, explain the process taken to find this equation.

Answer 1

@agent0smith @ranjeet619 can you help me with this please?

Answer 2

First find the distance from A (which is the focus) to that dashed line - this is the value of c (the distance from the center to the focus). You can find b using: c^2 = a^2 - b^2

Also find the coordinates of the center (h, k) - trace along the line from A, the center will be where you reach the vertical dashed line.

Find the distance from the center, the the vertex of the hyperbola - this is the value of a.

See pic:

Answer 3

Would be a bit easier with a bigger pic.

Then you just use the general equation for a horizontal hyperbola:
\[\Large \frac{ (x - h)^2 }{ a^2} - \frac{ (y- k)^2 }{ b^2} = 1\]

Answer 4

so what would the equation exactly be?

Answer 5

Find all those values and put them into the equation: c, (h, k), a.

Then use c^2 = a^2 - b^2 to find b.

Answer 6

I am lost on this \. can you please walk me though it so I can understand?!

Answer 7

See the pic, everything you need is there. It'd be easier to see with a bigger pic.

Find the length of the green line, that's c.

Find the length of the red line, that's a.

Find the coordinates of (h, k)

Answer 8

so c is 8 b is 4 and h,k are (-4,3)?

Answer 9

Yep, c=8, (h,k) is (-4, 3), did you mean a or b is 4? You can't get b from the pic, use c^2 = a^2 + b^2

Answer 10

yeah I mean a is 4

Answer 11

c^2 = a^2 + b^2, not minus like i said earlier (minus is for an ellipse)

Answer 12

okay then what..??

Answer 13

c=8, a=4, so
8^2 = 4^2 + b^2

Find b. Then plug all the numbers into: \[\Large \frac{ (x - h)^2 }{ a^2} - \frac{ (y- k)^2 }{ b^2} = 1\]

Answer 14

this is soo much!

Answer 15

Yep, finding the equations of ellipse/hyperbolas is a fair bit of work.

Answer 16

OK ill figure something out cause I don't have that much time left!/:

Answer 17

thanks anyways

Answer 18

Well all you need is b^2... then you're done

64 = 16 + b^2
so b^2 = 48

Now, a=4 so a^2=16, h= -4, k=3, b^2=48:

Answer 19

\[\Large \frac{ (x - h)^2 }{ a^2} - \frac{ (y- k)^2 }{ b^2} = 1 \]

Now just plug in all those numbers and that's it.

Answer 20

a^2=16, h= -4, k=3, b^2=48
\[\Large \frac{ (x - (-4))^2 }{ 16} - \frac{ (y- 3)^2 }{ 48} = 1\]

Answer 21

thanks!!!!!!!!!!!!!!!!!!