Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
enjc
Group Title
Write an equation of a curve that intersects at right angles every curve of the family y = ln x+C for every real value of k.
 5 months ago
 5 months ago
enjc Group Title
Write an equation of a curve that intersects at right angles every curve of the family y = ln x+C for every real value of k.
 5 months ago
 5 months ago

This Question is Open

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.0
In other words: you're asked to find a general equation of a line that is normal (perpendicular) to any given point of \(\ln x+C\). The normal line is perpendicular to the tangent line, which means the slope of the normal line is the negative reciprocal of the slope of the tangent. The slope of the tangent is given by the derivative. \[y=\ln x+C~~\Rightarrow~~\frac{dy}{dx}=\frac{1}{x}~~\Rightarrow~~\text{slope}_{\text{normal}}=x\] So for some point \((x_0,y_0)\) on \(y=\ln x+C\), that is, \((x_0,\ln x_0+C)\), the normal line has slope \(x_0\). Also, since it passes through \(x_0,\ln x_0+C\), it will have the equation \[y\ln x_0C=x_0(xx_0)~~\iff~~y=\ln x_0x_0(xx_0)+C\] I'm not sure where the \(k\) comes in; I don't really have any context for the problem. This is just how I would approach it.
 5 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.