Question

The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is

• A. 25x² – 144y² = 900
• B. 144x² – 25y² = 900
• C. 144x² + 25y² = 900
• D. 25x² + 144y² = 900

Answer 1

Answer: (A)

25x² – 144y² = 900

Answer 2

Let the equation $\frac{x^{2}}{a^{2}}$ – $\frac{y^{2}}{b^{2}}$ = 1

Given 2b = 5 Ž b = 5/2 and 2ae = 13

Ž ae = 13/2

Now b² = a²(e² – 1)

Ž b² = a²e² – a²

$\frac{25}{4}$ = $\frac{169}{4}$ – a² Ž a² = $\frac{144}{4}$

\ equation $\frac{x^{2}}{\frac{144}{4}}$ – $\frac{y^{2}}{\frac{25}{4}}$ = 1

25x² – 144y² = 900