This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Conic Section – 1”.
1. What method is used to draw an ellipse having a major and minor axis and 2 foci being at a distance apart?
a) Intersecting arcs method
b) Eccentricity method
c) Rectangular method
d) Oblique method
Explanation: This method uses the principle of locating the points on the ellipse such that the sum of this distance from the 2 foci is always constant and is equal to the length of the major axis, which is given.
2. What is the fixed point which is responsible for generating the conics?
Explanation: Focus is denoted by “F”. The foci F1 and F2 are 2 foci points used to define a closed curve like the ellipse.
3. The eccentricity for the hyperbola is ___________
Explanation: This is the ratio of the distance of any points on the curve from the focus to that of the directrix. It is usually denoted by “e”.
4. When two foci and one point on the ellipse are given then the property for an ellipse is _________
Explanation: As the ellipse is a closed curve two foci, F1 and F2, it can be described as the locus of a point moving in such a way that the sum of its distance from the foci is always a constant.
5. When the eccentricity or the distance of focus and directrix are given then the property is _________
a) F2A-F1A = constant
b) F1A+F2A = constant
c) e = F1A/AB<1
d) e = AB/F1A<1
Explanation: The hyperbola is the locus of a point moving in such a way that the ratio of its distance to the focus and to that of the fixed line or directrix is always greater than 1.
6. The length of the transverse axis in a hyperbola is equal to _________
a) the sum of the distance between points on a curve to foci
b) the product of the distance between points on a curve to the foci
c) the difference of the distance between points on a curve to the foci
d) the ratio of the distance between points on a curve to the foci
Explanation: As the hyperbola has 2 branches its left and right halves with 2 foci F1 and F2, the focus of any point on it can be described as the difference between its distances from the foci and is always a constant. If A is a point on the hyperbola, then F2A-F1A = constant. This constant distance is equal to the distance between the two vertices v1 and v2. It is known as the transverse axis of the hyperbola.
7. In a rectangular hyperbola, the angle between the 2 asymptotes is equal to _________
Explanation: The asymptotes, when extended, approach nearer to the hyperbola curves and will become tangential to them at infinity. The asymptotes and the angle between them are also used for drawing the hyperbola curves. When the angle between the asymptotes is 900, then the hyperbola is known as a rectangular or equilateral hyperbola.
8. The sum of internal angles of a regular polygon of n sides is equal to _________
a) (2n-4) x 900
b) (2n-4) x 1800
c) (n-4) x 900
Explanation: A regular polygon of n sides subtends a total angle of 3600 at the center, with n isosceles triangles meeting at it. The identical sides of each isosceles triangular are equal to the radii of the circle circumscribing the polygon and they subtend semi-internal angles at each end of the sides of the polygon.
9. When the eccentricity of a conic curve is smaller than 1, the curve known as _________
Explanation: The conic section is a curve obtained by cutting a right circular cone with the help of the plane in different positions related to the axis. The condition for an ellipse is the cutting plane should pass through all the generators.
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