Assignment 1 (C)
Subject: ENGINEERING GRAPHICS -I
Class F.E Division :- C
Topic :- Hyperbola
Select a suitable scale
Faculty:- Prof. D.B.Shelke

Q.1 For a perfect gas , the relation between the pressure P & Volume V in isothermal (constant temperature) expansion is given by PV = Constant. Draw the curve of isothermal expansion of an enclosed volume of gas if 3 m3 of the gas correspond to a pressure of 4 KN/m2 . Draw the graph P Vs V for pressure range 1 KN/m2 to 10 KN/m2. Determine graphically
(i) The Volume of gas at a pressure corresponding to 3 KN/m2.
(ii) The pressure corresponding to volume of 4.5 m3

Q.2 0.025 m3 of air at a pressure of 6 Kgf/cm2 absolute expands until its volume is 0.25 m3 .The relation between the pressure & volume is given by the formula PV=0.15. Construct the expansion curve .Choose pressure scale 1 cm = 0.5 Kgf/cm2 & Volume scale 1 cm = 0.05 m3 . Name the curve.

Q.3 Draw the locus of a particle moving in such a way that the product of its distance from two fixed lines, at right angles to each other is constant, if a point on the curve is 20 mm & 45 mm from lines. Name the curve and draw normal & tangent at any point to the curve.

Q.4 Two straight lines OA & OB make an angle of 75 0 between them, P is a point 40 mm from OA & 50 mm from OB. Draw hyperbola through P with OA & OB as asymptote . Determine its eccentricity & show the focus.

Q.5 A perfect gas follows the law PV=Constant .At a pressure 3 Kgf/cm2 absolute, the volume of gas being 2 m3. Draw the graph P Vs V for pressure range 1 Kgf/cm2 absolute to 10 Kgf/cm2 absolute .Name the curve.

Q.6 The asymptote of a hyperbola are inclined at 70 0 to each other . A point P on the curve is 20 mm & 26 mm from the asymptotes. Construct the curve showing at least 3 points on either side of P . Determine the eccentricity of the curve.

Q.7 Two points A & B are located on a plane sheet of paper and are 80 mm apart. A point P moves on the sheet such that difference of its distances from A & B always remains 40 mm. Draw locus of point P & also draw its directrix and asymptotes.

Q.8 The asymptotes of a hyperbola are at right angle to each other & a point P on the curve is at a distance of 25 mm from the asymptote .Draw the two branches of the hyperbola.