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Conic Sections Questions

Practice 17 Conic Sections questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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17
Total Questions
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Easy
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16
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Hard
Practice by Exam:Mathematics(14)Quantitative Aptitude(3)

About Conic Sections — practice questions, PYQs & concepts

Conic Sections is a frequently-tested topic on Mathematics, Quantitative Aptitude. ExamTest.live currently lists 17 Conic Sections questions spanning previous-year papers from 2026 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Conic Sections weight in competitive exams

Across our Conic Sections question bank, the largest sources are Mathematics (14) and Quantitative Aptitude (3). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 0 easy Conic Sections questions are available — build fluency before moving up.
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All Conic Sections Questions(1–17 of 17)

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Q1hardmcqQuantitative AptitudeGovernment Recruitment Exam Practice Paper2026
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A cylinder is intersected by a plane inclined at an angle of to its axis. What is the shape of the resulting cross-section?
Q2mediummcqQuantitative AptitudeCompetitive Exam2026
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What is the shape of the cross-section, when a cone is cut by a plane parallel to its slant height?
Q3mediummcqMathematicsAIEEE 20062026
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The locus of the vertices of the family of parabolas is:
Q4mediummcqMathematicsAIEEE 20062026
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In an ellipse, the distance between its foci is and the minor axis is . Then its eccentricity is:
Q5mediummcqMathematicsAIEEE 20072026
100% accuracy
The normal to a curve at meets the -axis at . If the distance of from the origin is twice the abscissa of , then the curve is a:
Q6mediummcqMathematicsAIEEE 20072026
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For the hyperbola , which of the following remains constant when varies?
Q7mediummcqMathematicsAIEEE 20072026
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The equation of a tangent to the parabola is . The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is:
Q8mediummcqMathematicsAIEEE2026
A focus of an ellipse is at the origin. The directrix is the line and the eccentricity is . Then the length of the semi-major axis is:
Q9mediummcqQuantitative AptitudeAdda2472026
When a cone is sliced by a plane parallel to its base, but not passing through its apex, what is the shape of the resulting cross-section?
Q10mediummcqMathematicsJEE Main2026
The equation of the circle passing through the foci of the ellipse , and having centre at is:
Q11mediummcqMathematicsJEE Main2026
Given: A circle, and a parabola, .Statement - I: An equation of a common tangent to these curves is .Statement - II: If the line () is their common tangent, then satisfies .
Q12mediummcqMathematicsAIEEE 20122026
An ellipse is drawn by taking a diameter of the circle as its semi-minor axis and a diameter of the circle as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is:
Q13mediummcqMathematicsAIEEE 20122026
Statement 1: An equation of a common tangent to the parabola and the ellipse is .Statement 2: If the line is a common tangent to the parabola and the ellipse , then satisfies .
Q14mediummcqMathematicsAIEEE2026
A parabola has the origin as its focus and the line as the directrix. Then the vertex of the parabola is at:
Q15mediummcqMathematicsAIEEE2026
The locus of a point moving under the condition that the line is a tangent to the hyperbola is:
Q16mediummcqMathematicsAIEEE-CBSE-ENG-032026
The foci of the ellipse and the hyperbola coincide. Then the value of is:
Q17mediummcqMathematicsAIEEE2026
An ellipse has as semi minor axis, and its foci and the angle is a right angle. Then the eccentricity of the ellipse is:

Frequently Asked Questions

How many Conic Sections questions are on ExamTest.live?▼
We have 17 Conic Sections questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Conic Sections MCQs free?▼
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Which exams include Conic Sections questions?▼
Conic Sections questions are commonly asked in Mathematics, Quantitative Aptitude. You can filter by exam using the links above.
How do I practice Conic Sections questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.