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- by Prabal Barahi 9 months ago

**Cone**:

To say it simply, cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point.

Mathematically, a surface obtained by generating a **generator** along a **fixed line** such that the **semi vertical angle (vertex angle)** is always **fixed**, is called a **cone** (or **right cone**).

We take double right cone for our better understanding.

Now, a surface obtained by the intersection of a cone (or right cone) with a plane is called **conic section**. The nature of conic sections (i.e. curves) depends upon the position of intersection of a cone and a plane:

· If the angle between plane and axis of cone is **right angle** then the conic section is a **circle**.

· If the angle between plane and axis of cone is **greater than the semi vertical angle **then the conic section is an **ellipse**.

· If the plane cuts the cone **parallel to a generator** then the conic section is a **parabola**.

· If the angle between plane and axis of cone is **less than the semi vertical angle **then the conic section is a **hyperbola**.

**Conic Section**:

We can define conic section as, a **locus** of a point which moves in a plane such that the **ratio** of distances from a **fixed point** to a **fixed straight line** is always a fixed **constant**. The fixed point is called **focus**. The fixed line is called **directrix**. The ratio of distances is called **eccentricity(e)**.

Now, on the basis of eccentricity; if:

- e = 1 i.e. PS = PM

then conic section is a**parabola**. - e < 1 i.e. PS < PM

then conic section is an**ellipse**. - e > 1 i.e. PS > PM

then conic section is a**hyperbola.** - e = 0

then conic section is a**circle.**

<If you find any difficulty or mistake, do reach out to me through the comment section or social media.>

<notes source: from Rakesh Kumar Jha (RK) sir and book>

<images from internet>

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