High yield5 mapped NDA questions
Build the idea
Conics are easiest when you identify orientation before using a formula. The sign pattern distinguishes ellipse and hyperbola; the unsquared variable identifies a parabola's axis. NDA commonly asks focus, eccentricity, latus rectum and tangent properties.
Concept
Conics are curves obtained by slicing a cone: the parabola, ellipse and hyperbola. Each has a standard equation, a focus–directrix definition, and an eccentricity e that classifies it.
Eccentricity is the single most-asked property.
Key Points & Formulas
- Parabola y² = 4ax: vertex (0,0), focus (a,0), e = 1.
- Ellipse x²/a² + y²/b² = 1 (a>b): e = √(1 − b²/a²), e < 1.
- Hyperbola x²/a² − y²/b² = 1: e = √(1 + b²/a²), e > 1.
- Length of latus rectum: parabola 4a; ellipse/hyperbola 2b²/a.
Worked Example
Q. Find the eccentricity of the ellipse x²/25 + y²/16 = 1.
a² = 25, b² = 16 (a>b).
e = √(1 − b²/a²) = √(1 − 16/25) = √(9/25) = 3/5.