Trace the curve:

Question

Trace the curve:

dls · Answer

$$\Huge ay^2=x(a^2+x^2)$$

dls · Answer

The information I have collected about this curve so far is that : 
It is symmetric about x axis and y axis.
But The domain of this function is x>0 i.e [0,infinity) therefore it is only symmetric about x axis.
It passes through origin.

dls · Answer

$$\Large \frac{dy}{dx}=\frac{a^2+3x^2}{2ay}$$
so if I Increase x and decrease y the slope should increase

dls · Answer

something like
|dw:1414665816913:dw|

ganeshie8 · Answer

domain could be < 0 if a is negative

ganeshie8 · Answer

unless the domain is a given..

dls · Answer

don't we assume a is a +ve constant?that is what im assuming since im doing this chapter.....

dls · Answer

lets just continue this assumption for a while

ganeshie8 · Answer

**assume** is a tricky word

ganeshie8 · Answer

okie

dls · Answer

so...

dls · Answer

am I roughly correct?

ganeshie8 · Answer

yes and notice that y' is positive when y> 0

and is strictly negative when y<0

dls · Answer

yeah..and the answer is a bit different that's what confuses me

ganeshie8 · Answer

also y' = 0 when x = +- a/sqrt(3)

dls · Answer

|dw:1414666425228:dw|
like kind of smooth there