Calculus
posted by Hannah .
Find the orthoganal trajectories of the family. Use a graphing utility to graph several members of each family.
y = Ce^x
What am I supposed to do here? Can someone point me in the right direction?

express C as a function of x and y:
C = ye^x
find y' implicitly
y'e^x  ye^x = 0
y' = y
so, for any point on the curve Ce^x, the slope is just y
On a perpendicular trajectory, the slope is 1/y
dy/dx = 1/y
y*dy = dx
y^2/2 = x+c
Thus parabolas opening to the left are orthogonal to the exponential curves.
Respond to this Question
Similar Questions

Calculus  Orthogonal Trajectories
Find the orthogonal trajectories of the family of curves: y = k*(e^x)  so k = y/(e^x) differentiating we get: 1 = k(e^x)*(dx/dy) 1/(dx/dy) = k(e^x) dy/dx = k(e^x)...substituting for k: dy/dx = (y/(e^x))*(e^x) … 
English expression
How many are there in Mina's family? There are five in her family: her father, her mother, her older brother Minsu, her younger brother Minho, and her. How many people are there in Mina's family? 
English
Let's survey your family members' TV viewing habits. 1. Find out TV programs your family like most. 2. Investigate how many hours they watch TV. 3. Each gathers the investigation result, and compares how different their family members' … 
PreCalculus
1) Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes. x+4/ x^2+x6. 2) Use a graphing utility to graph the function and determine the xintercepts … 
Algebra
Questions on piecewise function graphing Obviously I can't get help with the actual graphing here but I am hoping someone can push me in the right direction Problem: f(x) {4, if 0<=x<2} {5, if 2<=x<4} {6, if 4<=x<6} … 
Calculus
I'm supposed to find the limit as x approaches infinity of (2xsinx)/(x+cosx). I've thought about using the squeeze theorem, but I'm not sure it applies here. Can someone point me in the right direction? 
Basic Algebra
$5130 is to be divided equally among the members of a family group. Eight members of the family obtained knowledge of the loot and insisted their share. Determine the original number of family members. I don't want the answer just … 
Basic Algebra
$5130 is to be divided equally among the members of a family group. Eight members of the family obtained knowledge of the loot and insisted their share. Determine the original number of family members. 
Spanish
Which statement is not true about friendships in the Spanish speaking world? 
Calculus
Use a graphing utility to graph the polar equation shown below. r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = 5 to n = 5. As you graph these equations, you should see the graph change shape from a heart to a bell. I'm …