Question

Trace the curve:

Answer 1

\[\Huge ay^2=x(a^2+x^2)\]

Answer 2

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.

Answer 3

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

Answer 4

something like

Answer 5

domain could be < 0 if a is negative

Answer 6

unless the domain is a given..

Answer 7

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

Answer 8

lets just continue this assumption for a while

Answer 9

**assume** is a tricky word

Answer 10

okie

Answer 11

so...

Answer 12

am I roughly correct?

Answer 13

yes and notice that y' is positive when y> 0

and is strictly negative when y<0

Answer 14

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

Answer 15

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

Answer 16

like kind of smooth there