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Conic Sections

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Sections of a Cone

Subtopic

Sections of a Cone under Conic Sections for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If α=50∘\alpha = 50^{\circ} and β=50∘\beta = 50^{\circ}, and the plane does not pass through the vertex, we get a:

    A.

    Circle

    B.

    Parabola

    C.

    Ellipse

    D.

    Hyperbola

  2. 2.

    A point is a degenerate case of which conic section?

    A.

    Only a circle

    B.

    Only an ellipse

    C.

    A circle or an ellipse

    D.

    A hyperbola

  3. 3.

    If a plane is parallel to the generator of a cone, the angle β\beta is:

    A.

    90∘90^{\circ}

    B.

    0∘0^{\circ}

    C.

    Equal to α\alpha

    D.

    Greater than α\alpha

Download the worksheet for Conic Sections - Sections of a Cone to practice offline. It includes additional chapter-level practice questions.

Circle

Subtopic

Circle under Conic Sections for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The equation of a circle with diameter endpoints (−1,0)(-1, 0) and (1,0)(1, 0) is:

    A.

    x2+y2=1x^2 + y^2 = 1

    B.

    x2+y2=2x^2 + y^2 = 2

    C.

    x2+y2+2x=0x^2 + y^2 + 2x = 0

    D.

    x2+y2−2x=0x^2 + y^2 - 2x = 0

  2. 2.

    If the equation x2+y2+4x−6y+lambda=0x^2 + y^2 + 4x - 6y + \\lambda = 0 represents a circle of radius 44, find lambda\\lambda.

    A.

    -3

    B.

    3

    C.

    13

    D.

    5

  3. 3.

    The center and radius of the circle x2+y2=20x^2 + y^2 = 20 are:

    A.

    (0,0), 20

    B.

    (0,0), 2sqrt52\\sqrt{5}

    C.

    (0,0), 10

    D.

    (0,0), 5

Download the worksheet for Conic Sections - Circle to practice offline. It includes additional chapter-level practice questions.

Parabola

Subtopic

Parabola under Conic Sections for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the axis of symmetry for the parabola y2=18xy^2 = 18x?

    A.

    x=0x = 0

    B.

    y=0y = 0

    C.

    y=4.5y = 4.5

    D.

    x=4.5x = 4.5

  2. 2.

    What is the length of the latus rectum for the parabola x2=yx^2 = y?

    A.

    1

    B.

    4

    C.

    0.25

    D.

    2

  3. 3.

    The vertex of the standard parabola y2=4axy^2 = 4ax is always at which point?

    A.

    (a,0)(a, 0)

    B.

    (0,a)(0, a)

    C.

    (−a,0)(-a, 0)

    D.

    (0,0)(0, 0)

Download the worksheet for Conic Sections - Parabola to practice offline. It includes additional chapter-level practice questions.

Ellipse

Subtopic

Ellipse under Conic Sections for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the eccentricity of the ellipse x281+y272=1\frac{x^2}{81} + \frac{y^2}{72} = 1.

    A.

    1/31/3

    B.

    1/91/9

    C.

    2/32/3

    D.

    72/9\sqrt{72}/9

  2. 2.

    What are the coordinates of the foci for the ellipse x2144+y2169=1\frac{x^2}{144} + \frac{y^2}{169} = 1?

    A.

    (±5,0)(\pm 5, 0)

    B.

    (0,±5)(0, \pm 5)

    C.

    (0,±13)(0, \pm 13)

    D.

    (±12,0)(\pm 12, 0)

  3. 3.

    For a vertical ellipse where the major axis is on the y-axis, what is the relation between a,b,a, b, and cc (where b>ab > a)?

    A.

    a2=b2+c2a^2 = b^2 + c^2

    B.

    b2=a2+c2b^2 = a^2 + c^2

    C.

    c2=a2+b2c^2 = a^2 + b^2

    D.

    b=a+cb = a + c

Download the worksheet for Conic Sections - Ellipse to practice offline. It includes additional chapter-level practice questions.

Hyperbola

Subtopic

Hyperbola under Conic Sections for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the foci of the hyperbola y225−x211=1\frac{y^2}{25} - \frac{x^2}{11} = 1.

    A.

    (0,±6)(0, \pm 6)

    B.

    (±6,0)(\pm 6, 0)

    C.

    (0,±14)(0, \pm \sqrt{14})

    D.

    (±14,0)(\pm \sqrt{14}, 0)

  2. 2.

    Find the eccentricity of the hyperbola y21−x23=1\frac{y^2}{1} - \frac{x^2}{3} = 1.

    A.

    2

    B.

    3\sqrt{3}

    C.

    23\frac{2}{\sqrt{3}}

    D.

    4

  3. 3.

    What is the length of the conjugate axis of the hyperbola y216−x24=1\frac{y^2}{16} - \frac{x^2}{4} = 1?

    A.

    4

    B.

    8

    C.

    16

    D.

    2

Download the worksheet for Conic Sections - Hyperbola to practice offline. It includes additional chapter-level practice questions.