Determine the eccentricity of the hyperbola $d i s pl a y s t y l e 4 x^{2} - 9 y^{2} = 36$ .

medium 3 marks Class 11 · Mathematics · Conic Sections

Answer

√13 / 3

The correct answer is √13 / 3 — Eccentricity $e = c / a = \frac{13}{3}$ .

Step-by-step solution

Rewrite the equation in standard form: $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ by dividing both sides by 36.
Identify $a^{2} = 9$ , $b^{2} = 4$ for the hyperbola.
Compute $c^{2} = a^{2} + b^{2} = 9 + 4 = 13$ , hence $c = 13$ .
Eccentricity $e = c / a = \frac{13}{3}$ .

Common mistake: Using

e = c / a

for an ellipse or mixing

a

and

b

Concept tested: Hyperbola – eccentricity