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August 22, 2014

August 22, 2014

Posted by **justin** on Tuesday, October 16, 2007 at 10:10pm.

A tangent line is drawn to the hyerbola xy=c at a point P.

1) show that the midpoint of the line segment cut from the tangent line by the coordinate axes is P.

2) show that the triangle formed by the tangent line and the coordinate axes always has the same area, no matter where P is located on the hyperbola.

- math repost!! -
**Reiny**, Wednesday, October 17, 2007 at 7:52amlet p(a,c/a) be the point on the hyperbola

for xy=c

dy/dx = -y/x, so at P the slope = -c/a^2

equation of tangent line:

y - c/a = -c/a^2(x - a) which when simplified is

cx - a^2y=-2ac

for x-intercept, let y=0, then x = 2a

for y-intercept, let x=0, then y = 2c/a

1. take the midpoint of (0,2c/a) and (2a,0) and what do you get????

2. aren't your x and y intercepts the base and height of your triangle??

take area = 1/2 base*height

= .....

= c which is the constant of the original equation!!!

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