Ellipse Definition and 406 Threads

If the area enclosed by an ellipse 4x^2+y^2=1 and its cross section is perpendicular to the x-axis then its volume is? I don't have the slightest clue how to do this? Maybe solve for 2y^2=1-4x^2 set the integral equal to pi times the intergral of 1/4 to 1 of 1-4x^2?

"Radius" of an Ellipse a couple things I'm trying to fit together. First: a planet orbits a sun (positioned at one focus) at an certain speed. At any given time of year it will be at that same spot year after year... i have little clue how to make that work or solve for it. Second: i need...

is there a formula to find the circumference of an ellipse?

The quadrant of the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2} = 1. lying in the first quadrant, revolves about the line joining the extremities of the major and minor axis. Show that the volume of the solid generated is \frac{\pi a^2 b^2}{\sqrt{a^2+b^2}} (\frac{5}{3} - \frac{\pi}{2}). I tried...

An ellipse on the xy-plane has foci at (-41, 23) and (115, 42). The ellipse is tangent to the x-axis. What is the length of the major axis of the ellipse?

I have two integrals to give the circumference of an ellipse. I can't solve either. First, using rectangular coordinates, 1/2s=S{[1+(f'(x))^2]^(1/2)}dx taken from x=-a to x=a Since, y^2=b/a(a^2-x^2) 2y*y'=-2bx/a y'=-bx/(ay) [f'(x)]^2=(x^2)/(a^2-x^2) At this point, I'm already...