Question

Let $16x^2-3y^2-32x-12y=44$ represent a hyperbola. Then

• A. Length of the transverse axis is $2\sqrt{3}$
• B. Length of each latus rectum is $32/\sqrt{3}$
• C. Eccentricity is $\sqrt{19/3}$
• D. Equation of a directrix is $x=\frac{\sqrt{19}}{3}$

Answer 1

Answer: (A), (B), (C)

Length of the transverse axis is $2\sqrt{3}$
Eccentricity is $\sqrt{19/3}$
Length of each latus rectum is $32/\sqrt{3}$

$16(x-1{)}^2-3(y+2{)}^2=48$
so, $\frac{(x-1{)}^2}{3}-\frac{(y+2{)}^2}{16}=1$
Length of transverse axis $=2\sqrt{3}$
Length of $L.R=\frac{32}{\sqrt{3}}$.
$eccentricity=\frac{\sqrt{19}}{\sqrt{3}}$.
equation of directrix, $x=1+\frac{3}{\sqrt{19}}$