Textbook of Engineering Drawing, Second Edition

---------------'----------Geometrical Contructions 4.23

T

A B

2 3

40

70

Mg. 4.34 Construction of a Hyperbola

3. With centre F I and radius V 11, draw arcs on either side of the transverse a.xis.


4. With centre F2 and radius V), draw arcs intersecting the above arcs at PI' and P;,


5. With centre F2 and radius VII, draw arcs on either side of the transverse axis.


6. With centre FI and radius V 2 1, draw arcs intersecting the above arcs at QI' Q.


7. Repeat the steps 3 to 6 and obtain other points P 2' p12' etc. and Q2' Q12' etc.

8. Join the pointsPI,P 2 , P 3 , p;,P;,P~ andQI,Q2,Q3' Q;,Q~,Q~ forming the two branches of

hyperbola.

Note: To draw a tangent to the hyperbola, locate the point M which is at 20mm from the focus say
F 2' Then, join M to the foci F I and F 2' Draw a line IT, bisecting the <F I MF 2 forming the required
tangent at M.

To draw the asymptotes to the given hyperbola

Lines passing through the centre and tangential to the curve at infinity are known as asymptotes.

Construction (4.35)

1. Through the vertices V I and V 2 draw perpendiculars to the transverse axis.


2. With centre ° and radius OF I = (OF 2)' draw a circle meeting the above lines at P, Q and R,S.


3. Join the points P,O,R and S,O,Q and extend, forming the asymptotes to the hyperbola.

Note: The circle drawn with ° as centre and VI V 2 as diameters is known as auxiliary circle.
Asymptotes intersect the auxiliary circle on the directrix. Thus. Dl' DI and D2D2 are the two
directrices for the two branches of hyperbola.