# Lec2_Conic sectionsl.pptx - Conic Sections ENGR Joseph E...

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Conic Sections ENGR. Joseph E. Acosta, Ph.D. Assistant Professor

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Conic Sections The curves that we will learn in this section are conic sections They are the results of slicing a cone at various angles Circle, ellipse, parabola and hyperbola
Conic Sections Parabolas, circles, ellipses, hyperbolas

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The Circle The plane that intersects the cone is perpendicular to the axis of symmetry of the cone.

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The Ellipse The plane that intersects the cone is neither parallel nor perpendicular to the axis of symmetry of the cone and cuts through 2 “sides”
The Parabola The plane that intersects the cone is parallel to an element of the cone.

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The Hyperbola The plane that intersects the cone is parallel to the axis of symmetry of the cone.
Where do you see conics in real life?

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Orbiting satellites (including the earth and the moon) trace out elliptical paths
Many building and bridges use the ellipse as pleasing (and strong) shape

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Cooling Towers of Nuclear Power Plants
Cooling Towers of Nuclear Power Plants

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A circle with center ( h , k ) and radius r has length to some point ( x , y ) on the circle. Squaring both sides yields the center-radius form of the equation of a circle. 1.1 Circles A circle is a set of points in a plane that are equidistant from a fixed point. The distance is called the radius of the circle, and the fixed point is called the center . 2 2 ) ( ) ( k y h x r 2 2 ) ( ) ( k y h x r 2

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The Center is at C (0,0) The circle with center (0, 0) and radius r has the equation: x 2 + y 2 = r 2 Equation of a Circle C(0,0)
• Fall '19
• Conic section

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