Question

Length of the latusrectum of the hyperbola $xy-3x-4y+8=0$ is

• A. $4$
• B. $4\sqrt{2}$
• C. $8$
• D. $Noneofthese$

Answer 1

Answer: (B)

$4\sqrt{2}$

Hyperbola $=xy-3x-4y+8=0$

(add & sub $12$)

$x(y-3)-4(y-3)+8-12=0$

$(x-4)(y-3)=4$

It is in form XY$=c^2$

where X$=x-4$

Y$=y-3$

Latus rectum $=\frac{2b^2}{a}=2\left(a\right)$ [rectangular hyperbola $b=a$]

We know that

$a=\sqrt{2}.C$

L.R$=2\sqrt{2}\cdot C$

$=\mathrm{2.2.}\sqrt{2}$

$=4\sqrt{2}$.