real world applications of conic section ( parabolas, hyperbolas, ellipses, and circles )
We all always ask ourselves after a math class if its going to be used in real life or have any impact on us as humans. Here is one example of such question & the answer from one of our middle school Math class.
I of IV: real world applications:
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We all know that a conic section is the intersection of a "plane" and a "double right circular cone". By changing the angle and location of intersection we can produce a circle, ellipse, parabola or hyperbola ( or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines. parabola, 2 parallel lines, 1 line or no curve). Lets look at some real world applications of parabolas, hyperbolas, ellipses, and circles.
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II of IV: elliptical pool table
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" Enough of thought experiments lets build one " he says ! and we say " Thank you ! "
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III of IV: Differences between Conic Sections
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Interactive Graphs: From equations in the video ::
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The general equation for any conic section is
Ax2+Bxy+Cy2+Dx+Ey+F=0 where A,B,C,D,E and F are constants. As we change the values of some of the constants, the shape of the corresponding conic will also change. It is important to know the differences in the equations to help quickly identify the type of conic that is represented by a given equation. If B2−4AC is less than zero, if a conic exists, it will be either a circle or an ellipse. If B2−4AC equals zero, if a conic exists, it will be a parabola. If B2−4AC is greater than zero, if a conic exists, it will be a hyperbola. |
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Iv of IV: lets look at it logically using a flow chart :
