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CBSE Class 11 (Commerce) Straight Lines and Conic Sections — practice questions

Explore 152 free Straight Lines and 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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Straight Lines and Conic Sections questions and exercises with answers

Showing questions 1–30 of 152.

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 →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 →Which is given as an application of conic sections?Read the answer and worked solution →When the cutting plane is at ninety degrees to the axis, the section is a: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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