Excellent! I am using the the textbook Calculus for Scientists and Engineers, and the authors' explanation of drawing level curves with an ellipse was fantastically terrible. Thank you for contributing!
Thank you. This is the first video that explained this in detail. However, I am confused as to how the (a) and (b)'s you were getting out of the equations.
You just look them up. Circles have an equation x^2 + y^2 = radius^2. So an equation x^2 + y^2 = 4, would be a circle with radius 2. The equation he was using was in the form of an ellipse, and so you can just look up the general equation for an ellipse and then read of the answers. Works for parabolas as well. They are all varieties of "Conics". If you google that you will see what I mean.
@john Barre if I may try to answer, you are given two variables and finding the third. Z depends on X and Y so there are three variables, technically. The up or down depends on the function. Since they are x^2 and y^2 there can never be a negative Z because any number squared will be positive. so this will always go in positive z axis direction. if you are talking about the x^2+2y^2=z equation. This video helped me understand so much about level curves in a single video, thank you good sir, hope you are doing well.
Thank you so much. How did you know it was an ellipse so quickly, and can you always find the a & b values by set the equation equal to 1 and square rooting the denominator?
when creating the 3D graph from the level curve (the example problem you did of the elliptical parabola) how do you know which way the function extends (up or down)? because you're only given 2 variables... not 3.
