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Conic Sections and Parametric Equations — High School Pre-Calculus practice questions

14 multiple-choice questions and 15 flashcards on Conic Sections and Parametric Equations, about 9% of the High School Pre-Calculus bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-02 · how we write and review questions

What this chapter covers

Conic Sections and Parametric Equations is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 14 of the bank's 150 multiple-choice questions — roughly 9% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Conic Sections and Parametric Equations practice questions

6 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

How long is the major axis of x²/16 + y²/9 = 1?

  1. 4
  2. 6
  3. 8
  4. 16

Answer: C — 8

C) Correct — a = 4, and the major axis is 2a. A) Gives the semi-major axis a. B) Gives the minor axis, 2b. D) Uses a² instead of 2a.

What is the equation of the circle with center (−2, 3) and radius 5?

  1. (x + 2)² + (y − 3)² = 25
  2. (x − 2)² + (y + 3)² = 25
  3. (x + 2)² + (y − 3)² = 5
  4. (x − 2)² + (y − 3)² = 25

Answer: A — (x + 2)² + (y − 3)² = 25

A) Correct — (x − h)² + (y − k)² = r² with h = −2 and k = 3. B) Flips the signs of the center. C) Forgets to square the radius. D) Flips the sign of h only.

What are the asymptotes of x²/9 − y²/16 = 1?

  1. y = ±(3/4)x
  2. y = ±(16/9)x
  3. There are none
  4. y = ±(4/3)x

Answer: D — y = ±(4/3)x

D) Correct — For x²/a² − y²/b² = 1, the asymptotes are y = ±(b/a)x. A) Inverts b/a. B) Uses b²/a². C) Every hyperbola has two asymptotes.

Identify the conic 4x² + 9y² − 36 = 0.

  1. Circle
  2. Ellipse
  3. Hyperbola
  4. Parabola

Answer: B — Ellipse

B) Correct — It rewrites as x²/9 + y²/4 = 1. A) Needs equal coefficients on x² and y². C) Needs opposite signs on x² and y². D) Needs only one squared variable.

What does x = cos t, y = sin t for 0 ≤ t ≤ π trace?

  1. The upper half of the unit circle, counterclockwise from (1, 0)
  2. The whole unit circle
  3. The lower half of the unit circle
  4. The upper half, clockwise from (−1, 0)

Answer: A — The upper half of the unit circle, counterclockwise from (1, 0)

A) Correct — From t = 0 to π the point moves from (1, 0) over the top to (−1, 0). B) Needs 0 ≤ t < 2π. C) sin t ≥ 0 on [0, π], so y is never negative. D) Gets the direction of travel backward.

What does x = cos t, y = sin t for 0 ≤ t < 2π trace?

  1. A line
  2. The unit circle
  3. A parabola
  4. An ellipse with axes 2 and 1

Answer: B — The unit circle

B) Correct — x² + y² = cos² t + sin² t = 1. A) The point keeps a constant distance from the origin. C) Neither coordinate is the square of the other. D) Equal coefficients give a circle.

Conic Sections and Parametric Equations flashcards

4 cards from the 15 in this chapter.

What are the four types of conic sections?

Circle, ellipse, parabola, hyperbola.

What is the equation of a circle centered at (h, k)?

(x − h)² + (y − k)² = r².

What is the standard form of an ellipse centered at the origin?

x²/a² + y²/b² = 1, where a, b > 0.

What is the eccentricity of a parabola?

e = 1.

Practise the full chapter

These are a sample. The full Conic Sections and Parametric Equations chapter runs 29 items with per-chapter progress tracking, on the web and in the iOS app.

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