# [SOLVED] convert from implicit to parametric equation

• Mar 26th 2008, 08:20 AM
SuperGranny
[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, 08:49 AM
Opalg
Quote:

Originally Posted by SuperGranny
Can anyone help me with this convertion??
2x^2+y^2+4x-8y+14=0
..some step by step instructions would be also welcome;)

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 $2(x+1)^2 + (y-4)^2 = 4$.

Step 2. Divide by 4, so as to get 1 on the right-hand side: $\frac{(x+1)^2}2 + \frac{(y-4)^2}4 = 1$. 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 $x=-1+\sqrt2\cos\theta$, $y=4+2\sin\theta$.