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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Frequently Asked Questions

A conic section is the curve obtained by the intersection of a plane with a right circular cone. Depending on the inclination of the plane, the curve may be a circle, parabola, ellipse, or hyperbola.

The curves included are circle, parabola, ellipse, and hyperbola.

A conic is the locus of a point such that the ratio of its distance from a fixed point (focus) to its distance from a fixed line (directrix) is constant.

Eccentricity \(e\) is the constant ratio of the distance of any point on the conic from the focus to its distance from the directrix.

If \(e=0\), the conic is a circle; if \(e=1\), a parabola; if \(0<e<1\), an ellipse; if \(e>1\), a hyperbola.

The standard equation is \(x^2+y^2=r^2\), where \(r\) is the radius.

The general equation is \(x^2+y^2+2gx+2fy+c=0\).

The center is \((-g,-f)\) and the radius is \(\sqrt{g^2+f^2-c}\), provided \(g^2+f^2-c>0\).

A circle is real if \(g^2+f^2-c>0\).

A parabola is the locus of a point whose distance from a fixed point equals its distance from a fixed line.

The standard equation is \(y^2=4ax\).

The focus is \((a,0)\).

The directrix is \(x=-a\).

The length of the latus rectum is \(4a\).

An ellipse is the locus of a point such that the sum of its distances from two fixed points is constant.

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