NDA Maths · Free notes
Conics — NDA Maths
Conics is 40 NDA PYQs across 2017–2026, and almost every one is a matter of reading the standard form, then reading off a focus, directrix, eccentricity, or latus rectum. Parabola, ellipse and hyperbola are one family generated by slicing a cone, unified by a single number: the eccentricity. The notes teach in four movements, foundations first: (1) Conic Sections — the focus–directrix definition, what eccentricity means, how it classifies each curve, and how to identify a general second-degree equation; (2) Parabola — the standard forms y² = 4ax (and its rotations), vertex/focus/directrix, the latus rectum, the focal distance, and tangents/chords; (3) Ellipse — the standard form, foci and eccentricity (c² = a² − b²), the defining sum of focal distances, and finding the equation from given data; (4) Hyperbola — the standard form, foci and eccentricity (c² = a² + b²), and its parametric description. Fix the standard form and orientation first; everything else is a formula. Every PYQ is tagged.
The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.
Subtopic notes
Conic Sections — Identification & Eccentricity
7 PYQsEvery conic is the locus of points whose distance from a fixed focus is a constant multiple — the eccentricity e — of the distance from a fixed directrix. The value of e alone says which conic it is.
Parabola — Equation, Properties & Latus Rectum
14 PYQsA parabola (e = 1) is the set of points equidistant from a focus and a directrix; its standard form y² = 4ax fixes the vertex, focus, directrix, axis, and latus rectum from the single number a.
Ellipse — Foci, Eccentricity & Focal Distances
15 PYQsAn ellipse is the set of points whose two focal distances add to a constant 2a; its standard form x²/a² + y²/b² = 1 gives the axes, and c² = a² − b² locates the foci and the eccentricity.
Hyperbola — Foci & Eccentricity
4 PYQsA hyperbola is the same family with e > 1; its standard form x²/a² − y²/b² = 1 has foci a distance c from the centre where c² = a² + b² — note the PLUS, the one sign that flips from the ellipse.
Formula & revision sheet
12 formulas · 12 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
12 formulas · 12 gotchas across all subtopics — the exam-eve cheat-sheet
Formulas (3)
Watch out for (2)
- Ellipse and hyperbola use OPPOSITE sign relations→ Eccentricity Values & Comparing Conics
- A second-degree equation is not always a curve→ Identifying a General Second-Degree Equation
Formulas (4)
Watch out for (4)
- The sign of the linear term sets the direction→ Standard Forms & Their Elements
- Directrix of is , on the OTHER side of the vertex→ Standard Forms & Their Elements
- Parabola latus rectum is , not→ The Latus Rectum
- Focal distance is , not→ Focal Distance & Focal Chords
Formulas (3)
Watch out for (3)
- Major axis = larger denominator→ Standard Form, Foci & Eccentricity
- Constant focal sum is (major axis), not→ The Sum of Focal Distances
- Ellipse latus rectum is — semi-MINOR squared over semi-major→ Building the Ellipse from Given Data
Formulas (2)
Watch out for (3)
- Hyperbola uses PLUS: c² = a² + b²→ Standard Form, Foci & Eccentricity
- A hyperbola's eccentricity is always greater than 1→ Standard Form, Foci & Eccentricity
- traces a HYPERBOLA, not an ellipse→ Parametric Form & θ-Independent Properties
PYQ weightage by concept
12 concepts · 40 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
12 concepts · 40 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Eccentricity Values & Comparing Conics | 5 | 13% |
| Identifying a General Second-Degree Equation | 2 | 5% |
| What a Conic Is — Focus, Directrix, Eccentricityfoundation | — | — |
| Concept | PYQs | Share |
|---|---|---|
| Standard Forms & Their Elements | 5 | 13% |
| The Latus Rectum | 5 | 13% |
| Tangents & Chords of a Parabola | 3 | 8% |
| Focal Distance & Focal Chords | 1 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| The Sum of Focal Distances | 6 | 15% |
| Building the Ellipse from Given Data | 6 | 15% |
| Standard Form, Foci & Eccentricity | 3 | 8% |
| Concept | PYQs | Share |
|---|---|---|
| Standard Form, Foci & Eccentricity | 2 | 5% |
| Parametric Form & θ-Independent Properties | 2 | 5% |
Test yourself on Conics
15 past NDA questions from this chapter, timed at 19 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.