#### blackops23

##### Member

- Joined
- Dec 15, 2010

- Messages
- 428

- Gender
- Male

- HSC
- 2011

5x^2 - y^2 + 4xy = 18 ---(1), I have to sketch it.

Here's what I did:

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10x - 2yy' + 4y + 4xy' = 0

5x - yy' + 2y + 2xy' = 0

y' = [(2y+5x)/(y-2x)]

As 2x-y--> 0, y'-->inf

therefore, y=2x, sub in ---(1)

5x^2 - 4x^2 + 8x^2 = 18

9x^2 = 18

x^2 = 2

x= +/- sqrt(2)

vertical tangents at [sqrt(2), 2*sqrt(2)] and [-sqrt(2), -2*sqrt(2)]

let numerator = 0

2y + 5x = 0

y= -5x/2, sub back in --- (1)

eventually...

-45x^2 = 72, therefore NO TURNING POINTS

Let x = 0, y^2= -18, no y-intercepts

let y=0, 5x^2 = 18

therefore x-intercepts: (sqrt(18/5), 0) and (-sqrt(18/5), 0 )

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So I've got two points with vertical tangents and 2 x-intercepts, what else can I do? Perhaps find any possible asymptotes? If so how do I do that?

Help greatly appreciated, thanks