## Problem 3.2 Engineering Curves – Focal points of the ellipse are at 80 mm apart and the minor axis is of 60 mm length. Determine the length of major axis and draw the ellipse by concentric circle method.

**Procedure: **

**Procedure:**

* Step-1* Draw a horizontal axis of some suitable length. And mark a point 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 60 mm and give points C & D as shown into the figure.

* Step-3* Mark the points F

_{1}& F

_{2 }Which are focal points on the horizontal axis and are 80 mm apart from each other.

* Step-4* Measure the distance between the point F

_{1 }& C or D and with this distance keep O as center and cut the horizontal axis on both the sides and give points A & B, which is the major axis of the ellipse. Hence the distance of the major axis is 100 mm.

* Step-5* With O as center and radii equal to OC and OA or OD and OB draw two circles.

* Step-6* Divide these circles into 12 equal divisions as shown into the figure. And give the notations 1,2,3, etc. where these lines of divisions intersect the outer circle & 1’,2’,3’ etc. where these lines intersect the inner circle.

* Step-7* Draw vertical lines from the points 2,3,5,6, in downward directions and 8,9,11,12 in upward directions respectively.

* Step-8* Draw horizontal lines from the points 2’,3’,11’,12’ in left hand direction and from the points 5’,6’,8’,9’ in right hand direction respectively.

* Step-9* Give the notations p

_{1},p

_{2},p

_{3}etc. at the points of intersections of these horizontal & vertical lines respectively as shown into the figure.

* Step-10* Draw a smooth free hand medium dark curve from the points p

_{1},p

_{2},p

_{3}etc. in sequence, so the resulting curve is the ellipse.

* Step-11* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.