(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the implicit equation of the curve that goes through the point (3, 1) and whose tangent and normal lines always form with the x axis a triangle whose area is equal to the slope of the tangent line. Assume y` > 0 and y > 0.

2. Relevant equations

Hint: ∫( √(a^2 - u^2) / u du = √(a^2-u^2) - a*ln | [a+√(a^2-u^2)] / u | + C

(sorry, I don't know how to use the math writer yet)

3. The attempt at a solution

This is a question from an introductory differential equations class. I have absolutely no idea how to do this! I haven't really gotten anywhere yet. This is what I've done:

let f(x) denote the curve we're looking for. Then the tangent line will have equation:

y_t = df/dx * x + C

Normal line will have equation y_n = -1/(df/dx) * x + k

Together they will form a triangle with area = df/dx, at any point on f(x). I wanted to find an expression for area in terms of df/dx, simplify it, and solve the resulting differential equation, but I can't figure out a DE for the area! I'm getting very frustrated, as we've never been shown a question like this in lecture, and I can't find any examples in my textbook.

Help would be very much appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find curve with tangent and normal lines that create a triangle with given area

**Physics Forums | Science Articles, Homework Help, Discussion**