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) .

Ellipse Concentric Circle Method

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.

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Ellipse Rectangle Method

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.

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