Unit No. 1
ELLIPSE1. In a triangle ABC, AB, BC and AC are 100 mm, 50 mm and 75 mm resp. Draw an ellipse such that A and B are foci and C is the point on the curve. (S-10)
2. Draw an ellipse circumscribing rectangle of size 60mm x 40 mm.
3. A point P moves in such a way that sum of its distances from two fixed points A and B which are 90 mm apart remains constant, when P is at equal distances from A and B, its distance from each one is 75 mm. draw the path traced by the point P. (S-08)
4. A plot of land is in shape of parallelogram of 20m x 15 m. The angle included is 60°. Inscribe an elliptical flower bed in it. (W-2000)
5. Draw a vertical line OA = 30 mm, complete the traingle AOB with <AOB = 60° and length OB = 45 mm, treat 'O' as center of ellipse, OA as semi minor axis and 'B' a point on ellipse. Complete the ellipse and determine the eccentricity.
PARABOLA
1. An artillary gun fires a bombshell from ground surface to a target on the same level and 15 km away. The bombshell achieves maximum height of 5 Km. Draw the path traced by the shell selecting a suitale scale. Name the curve. (S-07)
2. AOB is a right angle triangle with AO = OB = 45 mm and <AOB = 90°. Draw a parabola passing through point A and B. (W-96).
HYPERBOLA
1. Two straight lines OA and OB make an angle of 75° between them, P is a point 40 mm from OA and 50mm from OB. Draw hyperbola through point P. (S-01)
2. Two points F and F' are located on a sheet of paper and are 100 mm apart. A point P moves on the sheet such that the difference of its distance from F and F' is always remain 60 mm. Find the locus of point P. (S-06)
CYCLOID
1. A coin 30 mm diameter rolls in a straight line on a table. Plot and name the locus of point lying on the circumference for one complete revolution. (S-06)
2. A vertical line AB of 50 mm long is a diameter of circle. The circle rolls without slipping on a horizontal line AC. Draw path traced out by point B for one complete revolution of a circle. Name the curve. (S-97)
3. A circle of 50 mm diameter rolls on a straight line without slipping . If initial position of diameter AB is parallel to the line in which it rolls. Draw the locus of point A for one revolution of circle. Name the curve. (W-03)
INVOLUTE
1. Draw the involute of a regular hexagon of side 20 mm. (W-07)
2. Draw a cicle with diameter AB equal to 65 mm. Draw a line AC 150 mm long and tangent to the circle. Trace the path of A, when the line AC rolls on the circle, without slipping. Name the curve. (W05)
3. trace the path of the end P of straight line Ap, 100 mm long when it rolls without slipping on the semicircle having its diameter AB, 75 mm long. The line Ap is tangent to the semicircle in the straight position.
4. A line AC of 150 mm long is tangent to the circle of diameter 60 mm. Trace the path of A and C, when line AC rolls on the circle without slip.(S-08)
5. A stick of length equal to the circumference of semicircle, is initially tangent to the semicircle of radius = 40 mm, on the right side of it. This stick now rolls over the circumference of a semicircle without slipping till it becomes tangent on the left side of semicircle. draw the locus of two end points of this stick. Name the curve. (S-11)
6. An inelastic string of 120 mm length has its one end is attached to the circumference of a circular disc with a 50 mm diameter. Draw the curve traced out by the other and of the string when it is completely wound round the disc keeping the string always tight. Name the curve. (W-11)
7. A composite figure consists of semi Hexagon of 30 mm side and a semicircle. A tread of length 165 mm is tied at one of the corner and wound on the periphery of the figure keeping it tight. Trace the curve generated by the free end of the tread P and name it.
ARCHEMEDIAN SPIRAL
1. A link OA, of 100 mm long rotates about O in clockwise direction. A point P on the link which is at 15 mm from O moves with uniform velocity and reaches end A, while the link rotates through one and half revolution. Trace the path of the point and name the curve.
2. Draw the archemedian spiral of one and half convolution of which A is pole and AB = 25 mm, AC = 30 mm and <BAC = 30°. B and C points lie on Archemedian spiral. (W-98)
3. Draw a triangle AOB with OA = 30 mm and OB = 50 mm <AOB = 120°. Draw an Archemedian spiral passing through point A and B with O as pole. Complete the curve starting from O.
4. A wheel if diameter AB = 120mm rotates about its center O. During its two complete rotation, a point P moves along AB from A to B and back to A. Draw the locus of point P. (S-98)
PROJECTION OF STRAIGHT LINE
1. A point A of line AB 70 mm long is 30 mm above HP and is in VP. Draw the projection of line if the line is inclined at 30° to HP and 45° to VP.
2. The top view of a 80 mm long line AB measures 55 mm, while the length of its front view is 70 mm. Its one ned is 15 mm above HP and 15 mm infront of VP. Draw its projrctions & determine its inclination with HP & VP. (W-07)
3. The top view of 75 mm long line Ab measures 65 mm, while the length of its FV is 50 mm. Its one ned A is in HP and 12 mm in front of VP. Draw the projections of AB and determine its inclination with HP and VP.
4. A line AB, 65 mm long has its end A 20 mm above the HP and 25 mm in front of VP. The end B is 40 mm above the HP and 65 mm in front of VP. Draw the projections of AB and show its inclinations with HP and VP.
5. A line AB, 90 mm long is inclined at 45° to the HP and its top view makes an angle of 60° with the VP. The end A is in HP and 12 mm in front of VP. Draw the front view and find the true inclination with the VP.
6. A line AB 90 mm long is inclined at 30° to HP. Its end A is 12 mm above the HP and 20 mm in front of VP its front view measures 65 mm. Draw the top view of AB and determine its inclination with VP.
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