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Show that the curves $2 x^{2}+3 y^{2}=5$ and $y^{2}=x^{3}$ are orthogonal.

Calculus 2 / BC

Chapter 16

First-Order Differential Equations

Section 3

Applications

Differential Equations

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Lectures

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In mathematics, integratio…

06:55

In grammar, determiners ar…

04:26

Show that the families of …

04:06

02:38

01:21

02:10

Show that the differential…

07:10

Prove that $r$ describes a…

08:24

Determine the orthogonal t…

09:36

07:21

Two curves are orthogonal …

08:17

Orthogonal Trajectories In…

this video, we're gonna go through the answer to question about 11 Chapter 16.3 The rest to show that the two Curves A and B written here off organo. It's a city that had been a show that the Grady in the Wadi Axe off a is equal to the negative reciprocal off the Grady in off Let's Start with a first. So let's differentiate at the equation given by A With respect to X, we're gonna have four X because at six while you got the X is equal to zero who had just used the train will seconds on the do that for Do I have the X? It's gonna be equal to minus X minus two x over three. Why Now? Let's think about the equation given by be different chasing this with respect to X, give us two. Why b y. The X is equal to three x squared. So therefore, do I The X It's gonna be ableto three x squared over two. Why rewrite this slightly? Let's have a think about having come right this equation be so we can write this as X squared is equal to why squared of X so just divide both sides by X, so we can then use that equation. Try this as three. Why squared number two? Why X We can cancel a why? From the denomination. The new Momenta. I would get three. Why over to you, X, and you'll see that three y over two x is the negative reciprocal of miners to accept three. Why? So that for

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