y=mx+c x y Cartesian Plane
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Chapter 10  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Conic Sections

Four Curves, Maximum Marks — The Crown Jewel of Coordinate Geometry

📋 50 MCQs ⭐ 0 PYQs ⏱ 60 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
20Medium
10Hard
0PYQs
60 secAvg Time/Q
2Topics
Easy 40% Medium 40% Hard 20%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSATKVPY

Conic Sections is the single highest-weightage chapter in Class XI for JEE — 5 to 7 MCQs per paper. JEE Advanced asks intricate tangent-chord-normal problems. Every BITSAT paper has 4–5 conic MCQs. KVPY loves parametric form problems. This is the largest MCQ bank in the series — spend maximum time here.

Topic-wise MCQ Breakdown

Parabola — Standard Forms30 Q
Parabola — Focus/Directrix20 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\mathrm{Parabola\ y²=4ax:\ focus\ (a,0),\ directrix\ x=−a}$
$\mathrm{Ellipse:\ c²=a²−b²,\ e=c/a<1}$
$\mathrm{Hyperbola:\ c²=a²+b²,\ e=c/a>1}$
$\mathrm{Tangent\ to\ y²=4ax:\ y=mx+a/m}$
$\mathrm{Chord\ of\ contact\ T=0}$

MCQ Solving Strategy

Build a single-page comparison table of all four conics: focus, directrix, eccentricity, tangent form, normal. For MCQs, identify the conic in ≤5 seconds by checking the equation pattern. For tangent MCQs, use the condition for tangency (slope form gives a/m directly). Parametric approach solves 80% of focal chord and chord of contact problems faster than Cartesian.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify conic, find vertex/focus/eccentricity from standard form

② Medium

Tangent condition, normal equation, focal length problems

③ Hard

Chord of contact, combined tangent-normal, locus of midpoint

★ PYQ

JEE Advanced — parametric tangent chains; JEE Main — 5 direct conic MCQs

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter 3D Geometry MCQs
🎯 Knowledge Check

Maths — CONIC SECTIONS

50 Questions Class 11 MCQs
1
The locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed line is called
(NCERT – Definition)
2
The fixed point associated with a parabola is called
(NCERT – Basics)
3
The fixed straight line used in defining a parabola is called
(NCERT – Basics)
4
The line passing through the focus and perpendicular to the directrix is called
(NCERT – Terminology)
5
The point where the parabola intersects its axis is called
(NCERT – Terminology)
6
The standard equation of a parabola with vertex at origin and axis along the x-axis is
(NCERT – Standard Forms)
7
In the equation \(y^2 = 4ax\), the focus is
(NCERT – Formula Based)
8
The directrix of the parabola \(y^2 = 4ax\) is
(NCERT – Formula Based)
9
The length of the latus rectum of the parabola \(y^2 = 4ax\) is
(NCERT – Formula Based)
10
The endpoints of the latus rectum of \(y^2 = 4ax\) are
(NCERT – Application)
11
The equation of a parabola opening upwards with vertex at origin is
(NCERT – Standard Forms)
12
The focus of \(x^2 = 4ay\) is
(NCERT – Formula Based)
13
The directrix of \(x^2 = 4ay\) is
(NCERT – Formula Based)
14
The axis of the parabola \(x^2 = 4ay\) is
(NCERT – Conceptual)
15
The vertex of the parabola \(y^2 - 8x = 0\) is
(NCERT – Direct)
16
The focus of the parabola \(y^2 - 8x = 0\) is
(NCERT – Direct)
17
The length of the latus rectum of \(x^2 = 12y\) is
(NCERT – Formula Based)
18
A parabola has focus \((0,3)\) and directrix \(y = -3\). Its vertex is
(NCERT – Reasoning)
19
The equation of a parabola with focus \((a,0)\) and directrix \(x = -a\) is
(NCERT – Deduction)
20
The parabola symmetric about the y-axis must have equation
(NCERT – Symmetry)
21
The distance of focus from vertex of the parabola \(x^2 = 16y\) is
(NCERT – Numerical)
22
The equation \(y^2 = -4ax\) represents a parabola opening
(NCERT – Conceptual)
23
The focus of \(y^2 = -12x\) is
(NCERT – Formula Based)
24
The directrix of \(x^2 = -20y\) is
(NCERT – Formula Based)
25
The parabola \(x^2 = 4ay\) passes through \((2a, a)\). The value of \(a\) is
(NCERT – Application)
26
The equation of the parabola with vertex at origin and focus at \((0,-2)\) is
(NCERT – Construction)
27
The latus rectum of a parabola is always
(NCERT – Property)
28
The number of tangents from the vertex of a parabola is
(NCERT – Conceptual)
29
The parabola \(y^2 = 4ax\) intersects the y-axis at
(NCERT – Geometry)
30
The eccentricity of a parabola is
(NCERT – Theory)
31
The distance between focus and directrix of \(y^2 = 20x\) is
(NCERT – Numerical)
32
The parabola \(x^2 = 4ay\) opens downward if
(NCERT – Conceptual)
33
The axis of the parabola \(y^2 + 4y - 8x = 0\) is parallel to
(NCERT – Analysis)
34
The vertex of \(y^2 + 4y - 8x = 0\) is
(NCERT – Completion of Square)
35
The focus of \(y^2 + 4y - 8x = 0\) is
(NCERT – Derived)
36
The equation \(x^2 - 6x - 4y = 0\) represents a parabola whose axis is
(NCERT – Identification)
37
The vertex of \(x^2 - 6x - 4y = 0\) is
(NCERT – Algebraic)
38
The focus of \(x^2 - 6x - 4y = 0\) is
(NCERT – Derived)
39
The length of latus rectum of \(x^2 - 6x - 4y = 0\) is
(NCERT – Formula Based)
40
A parabola always has
(NCERT – Property)
41
The distance of any point on a parabola from the focus equals its distance from
(NCERT – Definition)
42
The parabola \(y^2 = 4ax\) lies entirely in
(NCERT – Geometry)
43
The parabola \(x^2 = -9y\) opens
(NCERT – Direction)
44
The vertex of \(x^2 = -9y\) is
(NCERT – Direct)
45
The focus of \(x^2 = -9y\) is
(NCERT – Formula Based)
46
The directrix of \(x^2 = -9y\) is
(NCERT – Formula Based)
47
The parabola which is symmetric about the x-axis must have equation
(NCERT – Symmetry)
48
The number of axes of symmetry of a parabola is
(NCERT – Conceptual)
49
The parabola is a special case of
(NCERT – Theory)
50
The section of a right circular cone parallel to its generator gives
(NCERT – Advanced Concept)
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Class 11 Conic Sections MCQs (NCERT): 50 Questions with Answers
Class 11 Conic Sections MCQs (NCERT): 50 Questions with Answers — Complete Notes & Solutions · academia-aeternum.com
These multiple-choice questions are carefully designed to strengthen conceptual clarity and problem-solving skills in NCERT Class XI Mathematics, Chapter 10 – Conic Sections. Beginning with fundamental definitions and geometric intuition, the MCQs gradually progress to algebraic interpretation, analytical reasoning, and exam-oriented applications of circles, parabolas, ellipses, and hyperbolas. Each question reflects the NCERT pedagogy, emphasizing standard forms, focus–directrix properties,…
🎓 Class 11 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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