Thursday

July 24, 2014

July 24, 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!!!

**Related Questions**

math - A tangent line is drawn to the hyerbola xy=c at a point P. 1) show that ...

Math -Precal 11 - Show that the point P(7,7) is on the perpendicular bisector of...

Algebra please help! - I'm very confused with what I'm learning about right now...

Math (Pre Cal) - Hi, I am studying for a precalculus quiz and I do not ...

Math - Triangle with vertices: D(-18,12) E(-6,-12) F(12,6) Show that the right ...

Geometry Multiple Choice Question Please Help! - Find the value of x. If ...

Calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...

calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...

Math repost (please check) - L1=P1(1,3,5) and P2(4,5,2) L2=P4(-1,6,-3) and P3(...

Math - Each side of a triangle ABC is 75 units long. Point D is the foot of the ...