Question

The length of the latus rectum of the hyperbola xy - 3x - 3y + 7 = 0 is:

• A. 2
• B. 4
• C. 2$\sqrt{2}$
• D. None of these

Answer 1

Answer: (B)

4

Answer 2

x(y - 3) - 3 (y - 3) = 2

⇒ (x - 3) (y - 3) = 2

Let x - 3 = X and y - 3 = Y.

Equation of hyperbola ⇒ XY = 2 (rectangular hyperbola). In rectangular hyperbola a = b, so length of latus rectum

=$\frac{2b^{2}}{a} = 2a$ (distance between vertices) and xy = c², c²

= $\frac{a^{2}}{2} \Rightarrow 2 = \frac{a^{2}}{2} \Rightarrow a = 2$

(or) 2a = 4