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Conic Sections Practice Questions

JEE · Mathematics · 1742 free MCQs with instant results and detailed explanations.

1742
Total
373
Easy
791
Medium
578
Hard

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Topics in Conic Sections

Parabola 186
Ellipse 140
Hyperbola 131
Tangent 255
Normal 248
Chord 265
Eccentricity 210
Locus Problems 307

Sample Questions from Conic Sections

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
Which of the following is a property of a parabola?
A. It has two foci
B. It is symmetrical about two axes
C. It has one focus and one directrix
D. It is a closed curve
Show Answer & Explanation
Correct Answer: C
A parabola has one focus and one directrix which determine its shape and position.
Q2
Easy
In the parabola described by the equation 2y = x^2, what is the vertex?
A. (0, 0)
B. (1, 1)
C. (-1, 1)
D. (2, 2)
Show Answer & Explanation
Correct Answer: A
The vertex of the parabola is at the origin for this equation, which can be rewritten as y = (1/2)x^2.
Q3
Easy
Which of the following conic sections is described by the equation x^2 - 4y = 0?
A. Circle
B. Ellipse
C. Hyperbola
D. Parabola
Show Answer & Explanation
Correct Answer: D
The equation can be rearranged to y = (1/4)x^2, identifying it as a parabola due to its quadratic form in x.
Q4
Medium
If a parabola opens downwards and its vertex is at the origin, which of the following equations represents this parabola?
A. y = -x²
B. y = x²
C. y = -2x²
D. y = 2x²
Show Answer & Explanation
Correct Answer: A
A parabola that opens downwards has a negative coefficient for the x² term. The correct representation is y = -ax², where a > 0.
Q5
Medium
If the equation of a parabola is y^2 = 16x, find the coordinates of the focus.
A. (4, 0)
B. (0, 4)
C. (0, -4)
D. (2, 0)
Show Answer & Explanation
Correct Answer: A
The equation y^2 = 4px gives 4p = 16, hence p = 4. Thus, the focus at (p, 0) is (4, 0).
Q6
Medium
A parabola opens to the left with its vertex at (1, 2) and focus at (0, 2). What is the equation of the parabola?
A. (y - 2)^2 = -4(x - 1)
B. (y - 2)^2 = 4(x - 1)
C. (y - 1)^2 = -4(x - 2)
D. (x - 1)^2 = -4(y - 2)
Show Answer & Explanation
Correct Answer: A
The equation for left-opening parabolas is (y - k)^2 = -4p(x - h). Here, p = 1, leading to (y - 2)^2 = -4(x - 1).
Q7
Medium
If an ellipse is represented by the equation 9x^2 + 4y^2 = 36, find the coordinates of the vertices.
A. (3, 0) and (-3, 0)
B. (2, 0) and (-2, 0)
C. (4, 0) and (-4, 0)
D. (0, 2) and (0, -2)
Show Answer & Explanation
Correct Answer: A
Rewriting gives (x^2/4) + (y^2/9) = 1, with vertices located at (±a, 0) where a = 3.
Q8
Hard
For the parabola defined by x^2 = 16y, what is the distance from the vertex to the focus?
A. 2
B. 4
C. 8
D. 16
Show Answer & Explanation
Correct Answer: B
In this standard form, the distance is p = 4.
Q9
Hard
If the parabola given by y^2 = 16x has its vertex at the origin, what is the coordinates of its focus?
A. (4, 0)
B. (2, 0)
C. (0, 4)
D. (0, -4)
Show Answer & Explanation
Correct Answer: A
The focus is at (p, 0); here p = 4.
Q10
Hard
For the equation of parabola 3y^2 = 12x, identify the coordinates of the vertex.
A. (0, 0)
B. (4, 0)
C. (0, 4)
D. (3, 0)
Show Answer & Explanation
Correct Answer: A
This parabola is centered at the origin, so the vertex is (0, 0).

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Conic Sections — JEE Mathematics Practice Questions Online

This page contains 1742 practice MCQs for the chapter Conic Sections in JEE Mathematics. The questions are organized by difficulty — 373 easy, 791 medium, 578 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 8 topics, giving you comprehensive coverage of the entire chapter.