Can anyone help me with this convertion??

2x^2+y^2+4x-8y+14=0

..some step by step instructions would be also welcome;)

Thx

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- Mar 26th 2008, 07:20 AMSuperGranny[SOLVED] convert from implicit to parametric equation
Can anyone help me with this convertion??

2x^2+y^2+4x-8y+14=0

..some step by step instructions would be also welcome;)

Thx - Mar 26th 2008, 07:49 AMOpalg
This is not exactly step-by-step, but it will give you an outline of what's needed, and hopefully you can fill in the details.

__Step 1__. Collect the x terms together, and also the y terms, and complete the square in both x and y. That should lead to the result $\displaystyle 2(x+1)^2 + (y-4)^2 = 4$.

__Step 2__. Divide by 4, so as to get 1 on the right-hand side: $\displaystyle \frac{(x+1)^2}2 + \frac{(y-4)^2}4 = 1$. You should recognise that as the equation of an ellipse with its centre at (–1,4) and semi-axes √2 and 2 (the square roots of the denominators).

__Step 3__. You can then write down the parametric equations in the form $\displaystyle x=-1+\sqrt2\cos\theta$, $\displaystyle y=4+2\sin\theta$.