Question

How many conic sections are there?

Answer 1

Hint: Now we know that the conics are the curves which are obtained by intersection of the plane and a cone. Hence we will describe all the conics and their formation by intersecting plane and cone. Hence we have the number of conics obtained.

Complete step by step solution:
Now let us first understand what conic sections are?
Conic sections are curves which are obtained by intersection of plane and cone.
Hence with such a particular intersection we obtain three major curves which we refer to as conic sections.
The three types of surface that we get with the intersection are Parabola, Hyperbola and Ellipse.
Now let us first check how each curve is obtained using cones.
Check the diagram below to understand the figure and how is it obtained using the intersection of cone and plane.

Now hence we now know how Parabola, ellipse and hyperbola are formed.
Now for all the conic sections we have defined a line directrix and point focus.
A conic section is made with the help of this focus and the line directrix.
Now any point P on the curve of conics has distance from focus as constant multiple of the distance from directrix. If this constant is 1 the curve is parabola. If the constant is less than 1 then the curve is ellipse and if the constant is greater than 1 then we have the curve is hyperbola. This constant is called eccentricity and is denoted by e.

Note: Now note that a circle is also a curve in conic section. Circle is nothing but just an ellipse with a major axis equal to minor axis. If the plane cutting the cone is parallel to the surface of the cone then the conic obtained is a circle.