Asymptote of polar curve

**roshanhero** · August 19th 2008, 02:55 AM

Find the asymptote of

2r^2=tan2α
How to find it?

**mr fantastic** · August 19th 2008, 05:46 AM

Originally Posted by roshanhero

Find the asymptote of

2r^2=tan2α
How to find it?

Linear oblique asymptotes of the form $\alpha = \beta$ occur for values of $\alpha$ that make $\tan (2 \alpha)$ undefined.

And you know when $\tan (2 \alpha)$ is undefined, right .....?

**Soroban** · August 19th 2008, 09:15 AM

Hello, roshanhero!

Find the asymptotes of: . $2r^2\:=\:\tan2\theta$

In polar coordinates, asymptotes occur where $r \to \infty$

We have: . $r^2 \;=\;\frac{1}{2}\tan2\theta$

We see that asymptotes occur where: $2\theta \:=\:\frac{\pi}{2} + \pi n \quad\Rightarrow\quad \theta \:=\:\frac{\pi}{4} + \frac{\pi}{2}n$

**roshanhero** · August 20th 2008, 01:56 AM

I am terribly sorry,but I simply could not get it at all.I think I can easily find the horizontal,vertical and oblique asymptotes of the cartesian curve but I just don't have any concept regarding of finding asymptotes of the polar curve.Please explain it to me from the scratch.

**mr fantastic** · August 20th 2008, 04:58 AM

Originally Posted by roshanhero

I am terribly sorry,but I simply could not get it at all.I think I can easily find the horizontal,vertical and oblique asymptotes of the cartesian curve but I just don't have any concept regarding of finding asymptotes of the polar curve.Please explain it to me from the scratch.

What part of the discussion do you not understand? Do oyu know how to solve a trigometric equation such as $\cos (2 \theta) = 0$ ?

It may be that you're weak in the mathematical background assumed for these sorts of problems. In which case you're best advised to go back and revise the prerequisite mathematical concepts.

**roshanhero** · August 23rd 2008, 04:35 AM

We have been teached to find the asymptotes of polar curve by using formula-
Rsin(q -a )=1/f'(a )
Where a denotes the roots of f (q )=0
I appiled it but failed.
Can we show me how to do it by using this formula.

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