## Problem 3.6 Engineering Curves – Construct an ellipse by arcs of circle method. The major and minor axes are 140 mm & 100 mm respectively. Also draw the tangent and normal to the ellipse at any suitable point.

**Procedure:**

**Procedure:**

* Step-1* Draw a horizontal major axis of the length 140 mm and give the notations A & B as shown in the figure. And mark a midpoint O on it.

* Step-2* Draw a vertical axis, perpendicular to the horizontal axis & passing through the point O; of the length equal to the length of minor axis, which is 100 mm and give the notations C & D as shown in the figure.

* Step-3* With the center C or D and length equal to the half of the length of major axis; which is 70 mm; cut the major axis on two sides of the minor axis and give the notations F

_{1}& F

_{2}respectively as shown in the figure. These are the focal points of the ellipse.

* Step-4* Divide the distance between O & A into five equal divisions and give the notations 1,2,3 etc.

* Step-5* Now with the distance equal to A1 and center F

_{1 }draw an arc of sufficient length, and with the distance equal to B1 and center F

_{2 }cut the previously drawn arc on two sides of the major axis and give the notations P

_{1}& P

_{1}as shown in the figure.

* Step-6* Like in the above stated manner draw arcs with the distances A2 –B2, A3 – B3, A4 – B4 etc. and center F

_{1 }– F

_{2}respectively, which should intersect with each other respectively as shown in the figure. And give the notations as P

_{2}-P

_{2}, P

_{3}-P

_{3}, P

_{4}-P

_{4}etc.

* Step-7* Draw a smooth free hand medium dark curve through the points P

_{1}, P

_{2}, P

_{3}etc. as shown in the figure; in sequence, so the resulting curve is the ellipse.

* Step-8* Now mark a point anywhere on the ellipse; i.e., the point M, and connect this point with the focal points F

_{1}& F

_{2}with straight lines. Then bisect the angle F

_{1}MF

_{2}and draw a line of suitable length and give the notations N – N’ as shown in the figure. This is normal passing through the point M on the ellipse. Then draw a line which is tangent to the previously draw normal and give the notations T-T’, this is tangent passing through the point M on ellipse.

* Step-9* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.