#### Visualization of Conic Sections

Conic sections refer to the geometric figures obtained upon intersecting a cone with a plane making different angles with its axis. In polar coordinates, all conic sections are represented by a single equaion.

Length of Semi Latus-rectum

Eccentricity

##### Brief description

The equation of a conic with a semi latus-rectum length of 'L' and eccentricity of 'e' is given by

\[ r = \frac{l}{1 + e \cos \theta} \]The corresponding (r, θ) can be converted into cartesian coordinates (x, y) and plotted

**Circle**

When the plane is perpendicular to the conical axis, the conic section obtained is a circle. The semi latus-rectum is just the radius. Circles have an eccentricity of 0.

**Ellipse**

When the plane makes an angle more than the semi-vertical angle of the cone but less than 90^{o}, the conic section obtained is an ellipse. It like a bloated circle. Ellipses have an absolute eccentricity between 0 and 1 (exclusive).

**Parabola**

When the plane makes an angle lesser than the semi-vertical angle of the cone but intersections only a single motif, the conic section obtained is a parabola. They have an absolute eccentricity of 1

**Hyperbola**

When the plane intersects both the conical motifs, the conic section obtained is a hyperbola. They have an absolute eccentricity greater than 1.

**Note:**

- Due to their open-ended nature, parabolas and hyperbolas extend into infinity. They are not efficiently drawn here.
- Circles and Ellipses of huge lengths can be drawn. However, the curve may seem broken and a lot of time will be required to rescale
- All draw buttons are disabled during drawing and scaling

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