ENGINEERING CURVESCreate By :- bhilvala piyush m.

WHAT IS ELLIPSE?

• An Ellipse is a curve on a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse that has both focal points at the same location. 

• Ellipses are the closed type of conic section.

ELLIPSE SIPMLE DEFINATION• 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)For Ellipse E<1

HOW TO CREATE ELLIPSE?When the cutting plane is inclined to the axis but not parallel to

generator we get an ellipse as the section.

Section PlaneThrough Generators

Ellipse

EQUATIONSOF ELLIPSE?

• Equations

• Focus

• Eccentricity

• Area

  .   .

DRAWING METHOD OF ELLIPSE

• 1.Concentric Circle Method

• 2.Rectangle Method

• 3.Oblong Method

• 4.Arcs of Circle Method

• 5.Directrix Focus Method

CONCENTRIC CIRCLE METHOD

1

23

4

5

6

78

9

10

BA

D

C

1

2 3

4

5

6

7 8

9

10

RECTANGLE METHOD

1

2

3

4

1 2 3 4

1

2

3

4

3 2 1

C

D

OBLONG METHOD

C

D

1

2

3

4

1 2 3 4 3 2 1A B

1

2

3

4

ARCS OF CIRCLE METHOD

DIRECTRIX FOCUS METHOD

F ( focus)

DIR

E CT R

IX

V

ELLIPSE

(vertex)

A

B

30mm

45mm

APPLICATION OF ELLIPSE

• Elliptical reflectors and acoustics• Planetary orbits• Harmonic oscillators• Phase visualization• Elliptical gears• Optics• Ellipses in computer graphics• optimization theory

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