Posted by **Hannah** on Monday, March 5, 2012 at 10:43am.

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?

- Calculus -
**Steve**, Monday, March 5, 2012 at 1:11pm
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.

## Answer This Question

## Related Questions

- Pre-Calculus - 1) Use a graphing utility to obtain the graph of the function. ...
- English expression - How many are there in Mi-na's family? There are five in her...
- Basic Algebra - $5130 is to be divided equally among the members of a family ...
- Spanish - Which statement is not true about friendships in the Spanish speaking ...
- Basic Algebra - $5130 is to be divided equally among the members of a family ...
- English - Let's survey your family members' TV viewing habits. 1. Find out TV ...
- Calculus - Orthogonal Trajectories - Find the orthogonal trajectories of the ...
- Calculus - The present value of a building in the downtown area is given by the ...
- Calculus - The present value of a building in the downtown area is given by the ...
- Calculus - The present value of a building in the downtown area is given by the ...

More Related Questions