# Rectangular Hyperbola - Equ. of Tangents

• Apr 9th 2010, 09:01 PM
xwrathbringerx
Rectangular Hyperbola - Equ. of Tangents
Find the equations of tangents to xy = 3 parallel to y + 3x = 4. What is the distance between these tangents.

Hello.

How exactly do I find out the points on which the tangents touch the hyperbola?

Thank you.
• Apr 9th 2010, 09:21 PM
Sudharaka
Quote:

Originally Posted by xwrathbringerx
Find the equations of tangents to xy = 3 parallel to y + 3x = 4. What is the distance between these tangents.

Hello.

How exactly do I find out the points on which the tangents touch the hyperbola?

Thank you.

Dear xwrathbringerx,

First step is to differentiate xy = 3 with respect to x. Can you continue??
• Apr 9th 2010, 09:23 PM
xwrathbringerx
Dear Sudharaka

What's the point of differentiating the equ. of the hyperbola?

Isn't that only when you need to find the gradient of the tangents?
• Apr 9th 2010, 09:27 PM
Sudharaka
Quote:

Originally Posted by xwrathbringerx
Dear Sudharaka

What's the point of differentiating the equ. of the hyperbola?

Isn't that only when you need to find the gradient of the tangents?

Dear xwrathbringerx,

Because first you have to find the equation of tangents. For that you have to differentiate the equation of hyperbola. Then since we want tangents parallel to y=-3x+4 equate $\displaystyle \frac{dy}{dx}=-3$