math repost!!
posted by justin .
please help, i procrastinated and now this is due tomorrow!!
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.

let 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 xintercept, let y=0, then x = 2a
for yintercept, 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!!!
Respond to this Question
Similar Questions

Math Precal 11
Show that the point P(7,7) is on the perpendicular bisector of the line segment joining A (6,1) to B (0, 3). Also, verify that P is the same distance from A and B. For what values of k is the line y=l tangent to the circle (x3)^2 … 
Geometry
Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a twocolumn proof. Hint draw a DIAGRAM with the points labeled. Can some … 
math
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 … 
calculus
Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the xaxis. If the tangent point is close to the yaxis, the line segment is long. If the tangent … 
Geometry
Please write a paragraph proof for this statement. 30: Point Y is the midpoint of segment XZ. Z is the midpoint of segment YW. PRove that segment or line XY is congruent to segment or line ZW. 
Geometry
Please write a paragraph proof for this statement. Point Y is the midpoint of segment XZ. Z is the midpoint of segment YW. PRove that segment or line XY is congruent to segment or line ZW. 
math
A line segment has an endpoint at (3,2). If the midpoint of the line segment is (6.2), what are the coordinates of the point at the other end of the line segment? 
Calculus
Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the xaxis. If the tangent point is close to the yaxis, the line segment is long. If the tangent … 
Math
In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, … 
Calculus AB
Could someone please help me with these tangent line problems?