Question

Calculate equation of rectangular hyberbola with its focal length (128)^1/2

Answer 1

If xy = c is the equation of a rectangular hyperbola, what's the equation for the focal length?

Answer 2

Once you know it, set it equal to (128)^1/2 and solve.

Answer 3

c^2=a^2+b^2

Answer 4

how did u drive xy=c

Answer 5

ok

Answer 6

You need to know the eccentricity I think

Answer 7

yeh

Answer 8

Is it given in the problem?

Answer 9

noo

Answer 10

Ok then I typing the solution, with the letter e

Answer 11

Focal length of a hyperbola is ae, which according to you is equal to sqrt(128), then I think a is equal to {sqrt(128)/e}.
Since it is a rectangular hyperbola, a = b
So the equation to the hyperbola is
\[\frac{x^2}{\sqrt{128}/e}+\frac{y^2}{\sqrt{128}/e}=1\]

Answer 12

..............where e is the eccentricity. I need others' comment on this question, to be able to confirm if I am right in saying that the data of e should have been supplied by the question setter to make this question complete.

Answer 13

i guess e shud b eliminated sum ow

Answer 14

Wait. You asked about a hyperbola, not an ellipse. That is why I wrote down the equation of a hyperbola.

Answer 15

yeh i asked about hyperbola

Answer 16

the problem is, the equation above is the equation of an ellipse.

Answer 17

Oops! that equation with a -ve sign in the middle

Answer 18

which equation

Answer 19

n any case, there are two standard form for a hyperbola.

right ... the one I wrote down and then the one above corrected with a minus sign.

Answer 20

Focal length of a hyperbola is ae, which according to you is equal to sqrt(128), then I think a is equal to {sqrt(128)/e}.
Since it is a rectangular hyperbola, a = b
So the equation to the hyperbola is
\[\frac{x^2}{\sqrt{128}/e}-\frac{y^2}{\sqrt{128}/e}=1\]

Answer 21

i want e eliminated sum how, susanne give it a shot, n also check ur fan box