Ellipse Concentric Circle Method
Ellipse Rectangle Method

##
Defination of an Ellipse **:-**

It is a locus of a point moving in a plane such that the **sum** of it’s distances from **two** fixed points
always remains **constant** .
{And this sum equals to the length of major axis.}
These two fixed points are **focus 1** & **focus 2** .

**OR, in other words -**

These are the loci of points moving in a plane such that the ratio of it’s distances
from a fixed point And a fixed line always remains constant.
The ratio is called **eccentricity(E)** . The value for ellipse is less than one**(E<1)** .

**Problem 1** : Draw ellipse by concentric circle method.
Take major axis 100 mm and minor axis 70 mm long.

**Construction**

**Step 1.** Draw both the major & minor axes as perpendicular bisectors of each other.

**Step 2.** Taking their intersecting point as a center, draw two concentric circles considering both as respective diameters.

**Step 3.** Divide both circles in 12 equal parts & name as shown.

**Step 4.** From all points of outer circle draw vertical lines downwards and upwards respectively.
From all points of inner circle draw horizontal lines to intersect those vertical lines.

**Step 5.** Join all these intersecting lines along with the ends of both axes in smooth possible curve. It is required ellipse.

**Problem 2** :
Draw ellipse by Rectangle method.
Take major axis 100 mm and minor axis 70 mm long .

**Construction**

**Step 1. **Draw a rectangle taking major and minor axes as sides.
In this rectangle
draw both axes as perpendicular bisectors
of each other.

**Step 2.** For construction, select upper left part of rectangle. Divide vertical small side and horizontal long side into same number of equal parts.( here divided in four parts)

**Step 3.** Now join all vertical points 1,2,3,4, to the upper end of minor axis. And all horizontal points i.e.1,2,3,4 to the lower end of minor axis.

**Step 4.** Then extend D-1 line upto C-1 and mark that point. Similarly extend D-2, D-3, D-4 lines up to C-2, C-3, & C-4 lines.

**Step 5.** Mark all these points properly and join all along with ends A and C in smooth possible curve. Do similar construction in right side part along
with lower half of the rectangle. Join all points in smooth curve. It is required
ellipse.