Question

Hyperbole knowledge needed: What is the equation of tangent of hyperbole x^2/a^2 - y^2/b^2 = 1 in any point?

Answer 1

do you know how to perform implicit differentiation?

Answer 2

yes

Answer 3

that is what you need to do here in order to calculate dy/dx

Answer 4

I get the derivative b^2 (x / (sqrt(x^2 - a^2))) which is coefficient of direction of that tangent

Answer 5

that does not look correct to me

Answer 6

you may want to review implicit differentiation here first: http://www.youtube.com/watch?v=5yTVUZCaU6k

and then try again.

Answer 7

Ok, but am I correct that I should differentiate the equation of the hyperbole?

Answer 8

yes - you need to differentiate in order to calculate dy/dx - this will give you an expression for the slope of the tangent to this curve at any point along the curve.

Answer 9

This time I've got (a^2 b^2 - 2x b^2) / (-2 a^2 y) as a derivative.

Answer 10

I know that a condition for a line to be a tangent to hyperbole is n^2 = a^2 k^2 - b^2, where k is the slope and n is form equation y = kx + n, but since I don't have the exact coordinates of a point, I'm not sure how to determine the value of n.

Answer 11

Should I substitute it in that condition?

Answer 12

ok - next you do not need to use that condition you mentioned up there. I am not familiar with it but I believe you can solve this without any other knowledge