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Conic sections are the curves obtained when a plane cuts the cone. A cone generally has two identical conical shapes known as nappes. We can get various shapes depending upon the angle of the cut between the plane and the cone and its nappe. By cutting a cone by a plane at different angles, we get the following shapes:Circle, Parabola, Ellipse, and Hyperbola

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The circle is a special type of ellipse where the cutting plane is parallel to the base of the cone. The circle has a focus known as the center of the circle. 

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A circle is a closed curve that is drawn from the fixed point called the center, in which all the points on the curve are having the same distance from the center point of the center. 

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Pre Calculus: Finding the Equation of the Circle Given the Radius and Center

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The ellipse is one of the conic sections, that is produced, when a plane cuts the cone at an angle with the base. An ellipse is the set of all points (x,y) in a plane such that the sum of their distances from two fixed points is a constant. Each fixed point is called a focus (plural: foci) of the ellipse.

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The general form of the equation of an ellipse with center at (h, k) and length of the major and minor axes as '2a' and '2b' respectively. The major axis of the ellipse is parallel to the x-axis. 

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Writing Equations of Ellipses In Standard Form and Graphing Ellipses - Conic Sections

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A parabola is the curve formed by the intersection of a plane and a cone, when the plane is at the same slant as the side of the cone. When the intersecting plane is at an angle to the surface of the cone we get a conic section named parabola. It is a U-shaped conic section. 

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Finding The Focus and Directrix of a Parabola - Conic Sections

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A hyperbola is formed when the interesting plane is parallel to the axis of the cone, and intersect with both the nappes of the double cone. hyperbola is a conic section formed by intersecting a right circular cone with a plane at an angle such that both halves of the cone are intersected. This intersection produces two separate unbounded curves that are mirror images of each other.

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Another examples: Pizza, Ferris Wheel, Coin, Tire

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Real world example of Circle in Conic Sections 

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Real world example of Circle in Conic Sections 

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Real world example of Ellipse in Conic Sections 

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Real world example of Ellipse in Conic Sections 

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Real world example of Parabola in Conic Sections 

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Real world example of Parabola in Conic Sections 

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Real world example of Hyperbola in Conic Sections 

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Real world example of Hyperbola in Conic Sections 