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Punjab (PTB) · Chapter test · Free

2nd Year Mathematics Chapter 6 TestUNIT 6: CONICS

22 marks · 40 minutes · 18 questions. Covers: UNIT 6: CONICS.

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2nd Year Mathematics Chapter 6 Test

2nd Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 22Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. During the derivation of the standard equation of a horizontal ellipse, what is the defined algebraic relationship between constants a,b and c?

    1. b2=a2 +c2

    2. b2=c2 -a2

    3. b2=a2 - c2

    4. b2=a-c

  2. According to Kepler's first law, the orbits of the planets in the solar system follow which geometric shape?

    1. Circular

    2. Parabolic

    3. Elliptical

    4. Hyperbolic

  3. For the elliptical flower bed with a major axis of 10 m and minor axis of 6 m, what is its semi-major axis (a) and semi-minor axis (b)?

    1. a=10, b=6

    2. a=5, b=3

    3. a=25, b=9

    4. a=6, b=10

  4. A line that is perpendicular to a tangent line at its exact point of contact is defined as the:

    1. Normal

    2. Asymptote

    3. Directrix

    4. Axis

  5. If the elliptical arch of the bridge has a total width (span) of 24 meters, what are the coordinates of its vertices on the x-axis?

    1. (12,0) and (-12,0)

    2. (24,0) and (-24,0)

    3. (0,12) and (0,-12)

    4. (6,0) and (-6,0)

  6. Determine the geometric condition of the line y=2x-3 with respect to the ellipse ?

    1. The line is a tangent

    2. The line is a secant

    3. The line is external

    4. The line passes through the center

  7. The complete surface of a right circular cone consists of two separate parts called:

    1. Vertices

    2. Nappes

    3. Generators

    4. Axes

  8. What is the focus of the parabola ?

    1. (3,0)

    2. (0,3)

    3. (-3,0)

    4. (6,0)

  9. For a non-degenerate conic, if a line touches the conic at exactly one point, it is called a:

    1. Normal

    2. Secant

    3. Tangent

    4. Chord

  10. The equation of a normal can be readily obtained if you already know the equation of the:

    1. Parabola

    2. Directrix

    3. Axis of symmetry

    4. Tangent

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Find the equations of the circles passing through the points A(3,4) and B(3,-4) and touching the line x+2y+9=0.

  2. An ellipse has the following properties: The centre is at the point (3,-2). Find the standard equation of this ellipse.

  3. Find the equations of the tangent and normal to the circles: .

  4. A landscaper wants to create an elliptical flower bed with a major axis of 10 meters and a minor axis of 6 meters. Using the gardener's method, two stakes are placed at the foci, and a loop of string is stretched around them to trace the ellipse: (a) How far apart should the two stakes be placed? (b) What should be the total length of the string loop?

  5. Find the eccentricity of the hyperbola whose asymptotes are perpendicular.

  6. Find an equation of the ellipse with foci (2,1), (2,7) major axis of length 10 and sketch its graph.

  7. A parabolic arch has 120 m base and height 25 m. Find the height of the arch at a point 42 m from centre of the base.

  8. A circle has the parametric equation: . Find the Cartesian equation of the circle.