This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Conic Section – 2”.
1. Conic sections are the sections created by the intersection of ____________ by different relative positions of the plane to the axis.
a) Cylinder
b) Pyramid
c) Right circular cone
d) Trapezoid
View Answer
Explanation: Conic section is the curve, obtained by the intersection of a plane with the cone surface. Different conic sections are created by different positions of the plane relative to the axis of the cone.
2. Which curve is generated when the surface of a cone is intersected by a closed curve on one side of the apex?
a) Hyperbola
b) Parabola
c) Ellipse
d) Rectangular hyperbola
View Answer
Explanation: Ellipse is created when the surface of the cone is intersected by the closed curve on one side of the apex of the cone.
3. Which curve is generated when the surface of a cone is intersected by a closed curve parallel to the generating circle of the cone on one side of the apex?
a) Hyperbola
b) Parabola
c) Circle
d) Rectangular hyperbola
View Answer
Explanation: Circle is created when the surface of the cone is intersected by the closed curve parallel to the generating circle of the cone on one side of the apex of the cone.
4. _____________ is the conic created by the intersection of the plane parallel to one of the generators of the cone.
a) Hyperbola
b) Parabola
c) Circle
d) Rectangular hyperbola
View Answer
Explanation: The curve parabola is created by the intersection of the plane parallel to one of the generators of the cone to the surface of the cone.
5. When the cone is intersected by a plane parallel to the axis of the two cones that point towards one another.
a) Hyperbola
b) Parabola
c) Circle
d) Ellipse
View Answer
Explanation: The curve hyperbola is created by the intersection of the plane parallel to the axis of the cone to the surface of the cone.
6. Conic is a locus of points whose distance from a fixed point is a constant multiple of the distance from the fixed line. The fixed point is called_____
a) Point of start
b) Focus
c) Directrix
d) Start point
View Answer
Explanation: conic sections are in other way defined as the locus of points whose distance from a focus is a constant multiple of the distance from the directrix.
7. Conic sections are the locus of points whose distance from a focus is a constant multiple of the distance from the ________
a) Point of start
b) Focus
c) Directrix
d) Start point
View Answer
Explanation: Conic is a locus of points whose distance from a fixed point is a constant multiple of the distance from the fixed line. The fixed point is called focus and the fixed line is directrix.
8. Eccentricity (e) of the conic sections __________ when the distance of a point on the conic sections from the focus is f and the distance of the same point from the directrix is d.
a) d*f
b) d/f
c) f/d
d) d*f*0.5
View Answer
Explanation: conic sections are the locus of points whose distance from a focus is a constant multiple, that is eccentricity (e) of the distance from the directrix. Hence eccentricity of the conic sections(e) = \(\frac{distance \, of \, a \, point \, on \, the \, conic \, sections \, from \, the \, focus}{distance \, of \, the \, same \, point \, from \, the \, directrix}\).
9. Which of the following is true for ellipse? Eccentricity is indicated as e.
a) e<1
b) e>1
c) e=0
d) e=1
View Answer
Explanation: Eccentricity of the conic sections (e) = \(\frac{distance \, of \, a \, point \, on \, the \, conic \, sections \, from \, the \, focus}{distance \, of \, the \, same \, point \, from \, the \, directrix}\). For the ellipse the locus point distance from the focus is less than the distance from the directrix, hence e<1 for the ellipse.
10. Which of the following is true for the circle? Eccentricity is indicated as e.
a) e<1
b) e>1
c) e=0
d) e=1
View Answer
Explanation: Eccentricity of the conic sections (e) = \(\frac{distance \, of \, a \, point \, on \, the \, conic \, sections \, from \, the \, focus}{distance \, of \, the \, same \, point \, from \, the \, directrix}\), e<1 for ellipse and circle it is zero as the distance between the locus points and the directrix tends to infinity.
11. Which of the following is true for a parabola? Eccentricity is indicated as e.
a) e<1
b) e>1
c) e=0
d) e=1
View Answer
Explanation: Eccentricity of the conic sections (e) = \(\frac{distance \, of \, a \, point \, on \, the \, conic \, sections \, from \, the \, focus}{distance \, of \, the \, same \, point \, from \, the \, directrix}\), As the distance between locus point and the focus is equal to the distance between the locus point to the directrix.
12. Which of the following is true for a hyperbola? Eccentricity is indicated as e.
a) e<1
b) e>1
c) e=0
d) e=1
View Answer
Explanation: Eccentricity of the conic sections (e) = \(\frac{distance \, of \, a \, point \, on \, the \, conic \, sections \, from \, the \, focus}{distance \, of \, the \, same \, point \, from \, the \, directrix}\). For the hyperbola the locus point distance from the focus is greater than the distance from the directrix, hence e>1 for hyperbola.
13. The plane intersecting the cone during the formation of the circle is _______ to the axis of the cone.
a) Parallel
b) Perpendicular
c) 45° inclined to the axis
d) 30° inclined to the axis
View Answer
Explanation: Circle is the special case of an ellipse. It is created when the surface of the cone is intersected by the closed curve parallel to the generating circle of the cone on one side of the apex of the cone. Hence the intersecting plane is perpendicular to the cone axis.
14. In an ellipse, the line joining the foci is called ________ and its midpoint is the center of the curve.
a) Major axis
b) Minor axis
c) Principal axis
d) Semi-major axis
View Answer
Explanation: The line joining the foci is called as principal axis, its midpoint is the center of the curve. For ellipse and hyperbola, the principal axis is seen. The major and minor axis is the chords joining vertices.
15. Latus rectum is perpendicular to the directrix and passes through the focus.
a) True
b) False
View Answer
Explanation: The line which is parallel to the directrix and passing through focus is called latus rectum. The semi-latus rectum is the half of the length of the latus rectum and indicated by l in general.
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