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
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 $\displaystyle x=-1+\sqrt2\cos\theta$, $\displaystyle y=4+2\sin\theta$.