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Sri Vidya College of Engineering & Technology, Virudhunagar
Course Material (Lecture notes)
UNIT I
PLANE CURVES AND FREE HAND SKETCHING
CONIC SECTIONS
Definition:
The sections obtained by the intersection of a right circular cone by a cutting
plane in different positions are called conic sections or conics.
Circle:
When the cutting plane is parallel to the base or perpendicular to the axis,
then the true shape of the section is circle.
Ellipse:
When the cutting plane is inclined to the horizontal plane and perpendicular to
the vertical plane, then the true shape of the section is an ellipse.
Parabola:
When the cutting plane is inclined to the axis and is parallel to one of the
generators, then the true shape of the section is a parabola.
Hyperbola:
When the cutting plane is parallel to the axis of the cone, then the true shape
of the section is a rectangular hyperbola.
GE 6152 - Engineering Graphics - UNIT 1
Page 1 of 15

Sri Vidya College of Engineering & Technology, Virudhunagar
Course Material (Lecture notes)
Focus & Directrix:
Conic may be defined as the locus of a point moving in a plane in such away
that the ratio of its distances from a fixed point, called focus and a fixed straight line called
directrix.
Eccentricity:
The ratio of shortest distance from the focus to the shortest distance from the
directrix is called eccentricity.
For ellipse, eccentricity is
<1
For Parabola, eccentricity is = 1
For hyperbola, eccentricity is > 1
Axis: The line passing through the focus and perpendicular to the dirctrix is called axis.
Vertex: The point at which the curves cut the axis is called vertex.
GE 6152 - Engineering Graphics - UNIT 1
Page 2 of 15

Sri Vidya College of Engineering & Technology, Virudhunagar
Course Material (Lecture notes)
CONSTRUCTION OF ELLIPSE:
1. Draw an ellipse when the distance between the focus and directrix is 50mm
and eccentricity is 2/3.
Procedure:
Draw a perpendicular line AB (directrix) and a horizontal line CE (axis).
Mark the focus point F on the axis line 50mm from the directrix.
Divide the CF in to 5 equal parts.
As per the eccentricity mark the vertex ′V′ in the second division of CF
Draw a perpendicular line from vertex V and mark the point ′G′ with the distance VF.
Join the points C& G and extend the line. Similarly mark the point G1 below the axis
line.
Now join the points C& G1 and extend it.
Draw number of smooth vertical lines 1,2,3,4,5,6,etc., as shown in figure.
Now mark the points 1′, 2′, 3′, 4′, 5′…
Take the vertical distance of 11′ and with F as center draw an arc cutting the vertical
line 11′ above and below the axis.
Similarly draw the arcs in all the vertical lines (22′, 33′, 44′…)
Draw a smooth curve through the cutting points to get the required ellipse by free
hand.
GE 6152 - Engineering Graphics - UNIT 1
Page 3 of 15

Sri Vidya College of Engineering & Technology, Virudhunagar
Course Material (Lecture notes)
CONSTRUCTION OF PARABOLA:
2. Construct a parabola when the distance of the focus from the directrix is 40mm.
Note: Eccentricity, e = 1.
Procedure:
Draw a perpendicular line AB (directrix) and a horizontal line CE (axis).
Mark the focus point F on the axis line 40 mm from the directrix.
Divide the CF in to 2 equal parts.
As per the eccentricity mark the vertex ′V′ in the mid point of CF
Draw a perpendicular line from vertex V and mark the point ′G′ with the distance VF.
Join the points C& G and extend the line. Similarly mark the point G1 below the axis
line.
Now joint the points C& G1 and extend it.
Draw number of smooth vertical lines 1,2,3,4,5,6,etc., as shown in figure.
GE 6152 - Engineering Graphics - UNIT 1
Page 4 of 15

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