Question

The equation of the hyperbola in the standard form (with transverse axis along the x-axis) having the length of the latus rectum = 9 units and eccentricity = 5/4 is

• A. $\frac{x^{2}}{16} - \frac{y^{2}}{18}$ = 1
• B. $\frac{x^{2}}{36} - \frac{y^{2}}{27}$ = 1
• C. $\frac{x^{2}}{64} - \frac{y^{2}}{36}$
• D. $\frac{x^{2}}{36} - \frac{y^{2}}{64}$ = 1

Answer 1

Answer: (C)

$\frac{x^{2}}{64} - \frac{y^{2}}{36}$

Answer 2

$\frac{2b^{2}}{a^{2}}$ = 9 ⇒ 2b² = 9a ...(i)

Now b² = a²(e² – 1) = $\frac{9}{16}$a² ⇒ a = $\frac{4}{3}$b ......(ii), ($\because e = \frac{5}{4}$)

From (i) and (ii), b = 6, a = 8

Hence equation of hyperbola $\frac{x^{2}}{64} - \frac{y^{2}}{36}$ = 1