Question

The equation of the ellipse whose latus rectum is 8 and whose eccentricity is $\frac{1}{\sqrt{2}}$, referred to the principal axes of coordinates, is

• A. $\frac{x^{2}}{18} + \frac{y^{2}}{32} = 1$
• B. $\frac{x^{2}}{8} + \frac{y^{2}}{9} = 1$
• C. $\frac{x^{2}}{64} + \frac{y^{2}}{32} = 1$
• D. $\frac{x^{2}}{16} + \frac{y^{2}}{24} = 1$

Answer 1

Answer: (C)

$\frac{x^{2}}{64} + \frac{y^{2}}{32} = 1$

Answer 2

$\frac{2b^{2}}{a} = 8$ ….(i) Ž b² = 4a Ž a² (1 – e²) = 4a

Ž a(1 – e²) = 4 Ž a(1 – 1/2) = 4$\left\{ e = \frac{1}{\sqrt{2}} \right\}$ Ž a = 8

From (1) $\frac{2b^{2}}{8} = 8$ Ž b² = 32

\ eq. $\frac{x^{2}}{64} + \frac{y^{2}}{32} = 1$