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CBSE Class 11 (Commerce) Conic Sections — practice questions

Explore 100 free Conic Sections questions in CBSE Class 11 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Conic Sections questions and exercises with answers

Showing questions 1–30 of 100.

The equation y² = 4ax represents a PARABOLA with:Read the answer and worked solution →The eccentricity of a CIRCLE is:Read the answer and worked solution →The standard form of a circle with centre (3, -2) and radius 5 is:Read the answer and worked solution →The HYPERBOLA x²/a² − y²/b² = 1 has asymptotes given by:Read the answer and worked solution →By Kepler's First Law, every planet orbits the Sun in:Read the answer and worked solution →A satellite dish uses a parabolic reflector because:Read the answer and worked solution →The Cassegrain telescope design uses the reflective property of a:Read the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →Radians and degreesRead the answer and worked solution →True or false: reading the identitiesRead the answer and worked solution →Who gave the names parabola and hyperbola?Read the answer and worked solution →Conic sections are obtained by cutting which solid with a plane?Read the answer and worked solution →The cone used to define conics is described as double:Read the answer and worked solution →

Worked practice questions

The equation y² = 4ax represents a PARABOLA with:

  1. Focus at (0, a) and directrix y = -a (vertical)
  2. Focus at (a, 0) and directrix x = -a
  3. Focus at the origin (0, 0) always
  4. Focus at (4a, 0) and directrix x = 0
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Correct answer: B. Focus at (a, 0) and directrix x = -a

y² = 4ax: opens to the RIGHT. Focus at (a, 0), directrix x = -a (vertical line). Latus rectum length = 4a. For y² = -4ax (opens left), focus at (-a, 0).

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The eccentricity of a CIRCLE is:

  1. Equal to one (like a parabola)
  2. Greater than one (like a hyperbola)
  3. Equal to zero (special case)
  4. Between zero and one (like ellipse)
Show answer and solution

Correct answer: C. Equal to zero (special case)

**Circle:** e = 0 (all points equidistant from centre; foci coincide). **Ellipse:** 0 < e < 1. Parabola: e = 1. Hyperbola: e > 1. Circle is the limit of ellipse when foci merge.

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The standard form of a circle with centre (3, -2) and radius 5 is:

  1. $(x-3)^2 + (y+2)^2 = 25$
  2. $(x+3)^2 + (y-2)^2 = 25$
  3. $(x-3)^2 + (y-2)^2 = 5$
  4. $x^2 + y^2 + 6x - 4y - 4 = 0$
Show answer and solution

Correct answer: A. $(x-3)^2 + (y+2)^2 = 25$

**Standard form:** (x − h)² + (y − k)² = r². With (h, k) = (3, -2), r = 5: (x − 3)² + (y − (-2))² = 5² → (x − 3)² + (y + 2)² = 25.

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More Mathematics topics

StatisticsSequences and SeriesTrigonometric FunctionsBinomial TheoremSets, Relations and FunctionsLimits and DerivativesPermutations and CombinationsQuadratic Equations