Chapter 10 · Class XI Mathematics · NCERT Exercises

Conic Sections — Exercises

Circle · Parabola · Ellipse · Hyperbola — All NCERT Conic Solutions

📂 5 Exercises 📝 70 Questions 🎓 Very High

▶ Start Exercises 📖 Revise Notes

Exercise Index

Circle — standard & general form; centre & radius

Parabola — 4 forms; focus, directrix, latus rectum

Ellipse — a,b,c,e; foci, vertices, latus rectum

Hyperbola — a,b,c,e; foci, asymptotes

Mixed conics; find equation given conditions

5 exercise files · 70 total questions

Chapter at a Glance

JEE MainJEE AdvancedCBSE BoardsBITSATKVPY

18Concepts

40Formulas

Very HighDifficulty

10–14%Weightage

Before You Begin

Prerequisites

✓Ch 9 — Straight Lines
✓Completing the square in algebra
✓Coordinate geometry

Have Ready

🔧Conic comparison table
🔧Graph paper
🔧Compass for circles

Exercise Topic Map

Exercise 10.1(x−h)²+(y−k)²=r²; complete square on general form

Exercise 10.2y²=4ax (and 3 other parabolas); find focus, directrix, axis, LR

Exercise 10.3x²/a²+y²/b²=1; c=√(a²−b²); e=c/a<1; foci (±c,0); LR=2b²/a

Exercise 10.4x²/a²−y²/b²=1; c=√(a²+b²); e=c/a>1; asymptotes y=±(b/a)x

MiscellaneousGiven e and foci find equation; point on conic → find a,b

Key Formulae

\(\text{Circle: }(x-h)^2+(y-k)^2=r^2\)

\(y^2=4ax:\text{ focus}(a,0),\text{ directrix }x=-a,\text{ LR}=4a\)

\(\text{Ellipse: }c^2=a^2-b^2,\; e<1,\; LR=\tfrac{2b^2}{a}\)

\(\text{Hyperbola: }c^2=a^2+b^2,\; e>1,\; y=\pm\tfrac{b}{a}x\)

NCERT Solving Method

Step 1 — Identify conic type: both x²&y² same sign→circle/ellipse; only one squared→parabola; opposite signs→hyperbola. Step 2 — Extract a,b; compute c; find all elements systematically. Step 3 — Find equation given conditions: substitute focus/directrix/e into standard form. Step 4 — General form: always complete the square to convert to standard.

Continue Your Preparation

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