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AP Intermediate 1st Year Straight Lines and Conic Sections — practice questions

Explore 50 free Straight Lines and Conic Sections questions in AP Intermediate 1st Year 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 50.

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 →Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?Read the answer and worked solution →When solving a trigonometric equation, what is the CAST diagram used for?Read the answer and worked solution →Set the eccentricity of each conicRead the answer and worked solution →Split ellipse facts from hyperbolaRead 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 →Which section does the plane cutRead the answer and worked solution →Proper or degenerateRead the answer and worked solution →Sum, difference or equalRead the answer and worked solution →Type the conic termRead the answer and worked solution →Pop the conic sectionsRead the answer and worked solution →One word is wrongRead the answer and worked solution →Order by the tilt of the planeRead the answer and worked solution →Ellipse and hyperbolaRead the answer and worked solution →Which one does not belongRead the answer and worked solution →Sum or differenceRead the answer and worked solution →Spot the false statementRead the answer and worked solution →Which ones belongRead 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
Show answer and solution

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

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