Author Topic: ASX4Life Need's HELP! (Read 991 times) Tweet Share

Asx4Life · « **on:** October 30, 2011, 04:08:55 pm »

What is the shortest way to get the cartesian equation for x= t/(t^2+1) and y=1/(t^2+1)?

Mao · « **Reply #1 on:** October 31, 2011, 04:04:48 am »

Asx4Life · « **Reply #2 on:** October 31, 2011, 02:25:58 pm »

Quote from: Mao on October 31, 2011, 04:04:48 am

$x^2 = \frac{t^2}{(t^2+1)^2}$
$y^2=\frac{1}{(t^2+1)^2}$

$x^2+y^2 = \frac{t^2+1}{(t^2+1)^2}$

$\implies x^2 + y^2 = \frac{1}{t^2+1}$

$\implies x^2+y^2 = y$

Nice!!!
Thanks MAO. 1 more question, If VCAA asks for a cartesian equation, do I just have to get to the point where the equation is in terms of x and y. Or for example, in this question do I need to complete the square and get the general equation of an ellipse.

Mao · « **Reply #3 on:** October 31, 2011, 03:22:33 pm »

Quote from: Asx4Life on October 31, 2011, 02:25:58 pm

Quote from: Mao on October 31, 2011, 04:04:48 am
$x^2 = \frac{t^2}{(t^2+1)^2}$
$y^2=\frac{1}{(t^2+1)^2}$

$x^2+y^2 = \frac{t^2+1}{(t^2+1)^2}$

$\implies x^2 + y^2 = \frac{1}{t^2+1}$

$\implies x^2+y^2 = y$

Nice!!!
Thanks MAO. 1 more question, If VCAA asks for a cartesian equation, do I just have to get to the point where the equation is in terms of x and y. Or for example, in this question do I need to complete the square and get the general equation of an ellipse.

That would be preferable, yes.

nubs · « **Reply #4 on:** November 01, 2011, 02:42:18 pm »

Should you also specify the domain?

Mao · « **Reply #5 on:** November 01, 2011, 08:33:23 pm »

Quote from: Nirbaan on November 01, 2011, 02:42:18 pm

Should you also specify the domain?

It would also be preferable. However, the domain of x would be hard to find. (If you plot it, you will find $x\in [0,0.5]$ and $y\in (0,1]$ )

You can also get these domains from the cartesian equation $4x^2 + 4(y-0.5)^2 = 1$

$\implies \left( \frac{x}{0.5}\right)^2 + \left( \frac{y-0.5}{0.5}\right)^2 = 1$

Which is a circle centered around (0,0.5) with a radius of 0.5. Since both x and y must be positive, you take the portion in the first quadrant

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Author Topic: ASX4Life Need's HELP! (Read 991 times) Tweet Share

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