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## Homework Statement

Two curves are said to be orthogonal if their derivatives are opposite reciprocals at the point where the two curves intersect. Are 2x^2 + y^2 =3 and x= y^2 orthogonal?

## Homework Equations

I'm not entirely sure what to put here, but I think one relevant thing is to say that the two curves will intersect if they have slopes that are perpendicular to each other. (so m2= -1/m1)

## The Attempt at a Solution

Ok- so from what I can piece together, the first thing would be to find out if the two equations would have perpendicular slopes. So I would have to differentiate both equations to find their slopes.

so- 4x+ 2y= 0

and

1=2y

From here though, I am lost. I think y=.5 and x= -.25 and that m1=0 and m2=1. So my hunch is that these lines are not orthogonal. However, I am not sure if this is the correct thing to do. I have searched throughout my book and have not found any example problems worded like this. And related problems I found on the internet didn't make much sense to me.

First post here, so I hope I followed the form correctly. Any help or explanations of how to approach this problem would be very appreciated. Thank you for reading!

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