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**1. The problem statement, all variables and given/known da**

##\frac{x^{2}}{k^{2}} + \frac{y^{2}}{\frac{k^{4}}{4}} = 1## with k != 0

this can be simplified to

##x^{2} + 4y^{2} = k^{2}##

Find dy/dx implicitly, then find the new dy/dx if you want orthogonal trajectories to the ellipse. Lastly solve the differential equation and ifentify the orthogonal trajectories on the ellipse.

## The Attempt at a Solution

##2x + 8y\frac{dy}{dx} = 0##

now I know that for it to be orthogonal you need -dx/dy, so rearranging for dy/dx would give

## \frac{dy}{dx} = \frac{-x}{4y} ##

and -dx/dy is

## \frac{-dx}{dy} = \frac{4y}{x} ##

but my question is wouldn't you be losing solutions for y=0 and x=0? How would you account for that in the solution?