Question

A hyperbola passes through the points (3, 2) and (-17, 12) and has its centre at origin and transverse axis is along x-axis. The length of its transverse axis is

• A. 2
• B. 4
• C. 6
• D. None of these

Answer 1

Answer: (A)

2

Answer 2

Let the equation of hyperbola is $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}$ = 1

But it passes through (3, 2) ⇒ $\frac{9}{a^{2}} - \frac{4}{b^{2}} = 1$ ...(i)

Also its passes through (-17, 12)

⇒ $\frac{( - 17)^{2}}{a^{2}} - \frac{(12)^{2}}{b^{2}}$ = 1 ... (ii)

Solving these, we get a = 1 and b = $\sqrt{2}$

Hence length of transverse axis = 2a = 2.