completing the square with two variables, and application to ellipse equation

I show an example of completing the square in an expression with two variables, and go on to an application to putting an ellipse equation in standard form.

[ericabaez]

I love that I can see the logic behind it, not just applying formulas and steps mindlessly.

[glennmacneil]

Thank you so much. I was working on a simpler problem involving a circle and have not done this kind of math in years. Thanks for the help

[Shubham-cxrd]

You know what you had cleared my dought which is there I have since last two days
Thank you..
I hope you so active on YouTube again

[davidmetzler]

When they are joined, it's trickier. You have to use combinations such as (x+y), and usually you will need irrational coefficients. It's equivalent to diagonalizing a symmetric matrix. It's something that ideally I should teach but most books at the level I use tend to avoid it.

[ilkinond]

What happens when you have a term in xy? I can find nothing for this on the Internet although Spivak Calculus has such a problem in Chapter 1.

[joeface]

Thank you so much
You really helped me understand it

[Hawkstrike]

Could u do this
Identify the conic section: x^2-4x+y^2=2y= -1 if it is a parabola give the vertex, if it is a cirlce give the center and radius, if it is a ellipse or hyperbola give the center and foci
if u figure it out that would be hlepful thnxs