Engineering graphics lab Questions on Engineering Curve

Very important

1. Engineering Curves

2. Conic sections A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

3. Fig. B lack boundaries of the colored regions are conic sections.

4. When the section plane is inclined to the axis and cuts all the generators on one side of the apex, the section is an ellipse The inclination of the cutting plane for an ellipse should be greater than half of the apex angle Ellipse

5. Applications Astronomy The orbits of planets and comets around the sun are elliptical in shape. 

6. Engineering In engineering, ellipses are used in the design of certain types of arches and bridges. The elliptical shape provides a strong and stable structure

7. Parabola When the section plane is inclined to the axis and is parallel to one of the generators, the section is a parabola Parabola When the cutting plane is inclined to the axis and is parallel to one of the generators of the cone, the section is a parabola. The inclination of the cutting plane is equal to half of the apex angle,

8. Fig Formation of a hyperbola by cutting a cone Hyperbola When the cutting plane cuts both the parts of the double cone, the section is a hyperbola. The cutting plane for the hyperbola should not pass through the apex and its inclination should be less than half of the apex angle,

9. A parabola can be constructed by the following methods: 1. Eccentricity method 2. Offset method 3. Tangent method 4. Oblong method (a) Rectangle method (b) Parallelogram method

10. The major axis of an ellipse is 110 mm and minor axis is 70 mm long. Draw an ellipse by concentric circle(circles share the same Centre) method. Inscribe the largest possible ellipse in a rectangle of sides 160 mm and 100 mm. The conjugate diameters of an ellipse are 120 mm and 80 mm. The included angle between them is 75 o . Draw an ellipse by parallelogram method

11. Draw a parabola when the distance between its focus and directrix is 50 mm. Also, draw a tangent and a normal at a point 70 mm from the directrix. A parabolic arch has a span of 160 mm and a maximum rise of 100 mm. Draw a curve using offset method. Draw a parabola of base 120 mm and axis 80 mm by oblong method.

12. Fig. Formation of a rectangular hyperbola by cutting a cone

13. CONSTRUCTION OF HYPERBOLA A hyperbola can be constructed by the following methods: 1. Eccentricity method 2. Intersecting arcs method 3. Oblong method 4. Intercept method 5. Asymptotes method (a) Orthogonal asymptotes method (b) Oblique asymptotes method

14. 1.Draw a hyperbola when the distance of its focus from its directrix is 50 mm and eccentricity is 3/2. Also, draw a tangent and a normal to the hyperbola at a point 25 mm from the directrix. 2.Draw a hyperbola when half the trans verse axis, double ordinate and abscissa are 50 mm, 120 mm and 40 mm long respectively.