My graphic from yesterday has been extended to include foci and the related hyperbola with their asymptotes. I will leave it to your imagination and knowledge to identify how the foci, asymptotes, and hyperbola can be connected to the animation.
Wednesday, December 10, 2014
Sunday, December 7, 2014
More on Ellipses!
An expansion on an earlier post (December 5)
Every ellipse can be constructed by rotating two points on concentric circles at the same rotational speed in opposite directions, and tracing the midpoint of the segment between them. This sketch shows the process for horizontal and vertical ellipses.
Every ellipse can be constructed by rotating two points on concentric circles at the same rotational speed in opposite directions, and tracing the midpoint of the segment between them. This sketch shows the process for horizontal and vertical ellipses.
Saturday, December 6, 2014
Know the Quadratic Formula!!!
The Common Core does correctly propose that each student should
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.(see here)
The entire process is here.
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.(see here)
The entire process is here.
Friday, December 5, 2014
Ellipses a different way
Every ellipse can be constructed by rotating two points on concentric circles at the same rotational speed in opposite directions, and tracing the midpoint of the segment between them. Here, the two points Drag1 and Drag2 are movable on the x-axis. This particular file is restricted to horizontal ellipses.
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