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KCET Conic Sections — practice questions — page 2

Explore 104 free Conic Sections questions in KCET 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 31–60 of 104.

Find focus and directrix of parabola y² = -8x:Read the answer and worked solution →Eccentricity of hyperbola 9x² - 16y² = 144:Read the answer and worked solution →Length of latus rectum of ellipse x²/25 + y²/9 = 1:Read the answer and worked solution →Common tangent to circle x² + y² = 5 and parabola y² = 8x:Read the answer and worked solution →Eccentricity of ellipse: x² + 4y² = 4:Read the answer and worked solution →For parabola y² = 4ax, point (at², 2at) gives parametric form. If t = 2 and a = 3:Read the answer and worked solution →Sum of distances from any point on ellipse 9x² + 16y² = 144 to its foci:Read the answer and worked solution →Difference of focal distances from any point on hyperbola x²/16 - y²/9 = 1:Read the answer and worked solution →For hyperbola x²/25 - y²/144 = 1, find length of conjugate axis:Read the answer and worked solution →Auxiliary circle of ellipse x²/a² + y²/b² = 1:Read the answer and worked solution →Relation between eccentricities of conjugate hyperbolas:Read the answer and worked solution →Match the trig identity to its resultRead 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 →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →

Worked practice questions

Find focus and directrix of parabola y² = -8x:

  1. Focus (0, -2)
  2. No focus
  3. Focus (-2, 0), directrix x = 2 (opens left, a = -2)
  4. Focus (2, 0), directrix x = -2
Show answer and solution

Correct answer: C. Focus (-2, 0), directrix x = 2 (opens left, a = -2)

y² = -8x → 4a = -8 → a = -2. Vertex (0, 0), opens left. Focus (a, 0) = (-2, 0). Directrix x = -a = 2.

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Eccentricity of hyperbola 9x² - 16y² = 144:

  1. 3/4
  2. sqrt(7)/4
  3. sqrt(2)
  4. 5/4 (a² = 16, b² = 9, c² = 25, e = c/a = 5/4)
Show answer and solution

Correct answer: D. 5/4 (a² = 16, b² = 9, c² = 25, e = c/a = 5/4)

Rewrite: x²/16 - y²/9 = 1. a² = 16, b² = 9, c² = a² + b² = 25, c = 5. e = c/a = 5/4 = 1.25.

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Length of latus rectum of ellipse x²/25 + y²/9 = 1:

  1. 4
  2. 10
  3. 6
  4. 18/5 (= 2b²/a)
Show answer and solution

Correct answer: D. 18/5 (= 2b²/a)

For ellipse: latus rectum = 2b²/a = 2(9)/5 = 18/5 = 3.6.

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