Question

For the given hyperbola $9x^2-16y^2+18x+32y-151=0$, which of the following options is/are true:

• A. Centre of hyperbola is $(-1,1)$.
• B. Length of transverse axis is $8$ units.
• C. Length of conjugate axis is $6$ units.
• D. Eccentricity of hyperbola is $3$.

Answer 1

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

The correct options are
A Centre of hyperbola is $(-1,1)$.
B Length of transverse axis is $8$ units.
C Length of conjugate axis is $6$ units.

$9x^2-16y^2+18x+32y-151=0$
$\Rightarrow 9(x^2+2x+1)-16(y^2-2y+1)=144$
$\Rightarrow \frac{(x+1{)}^2}{16}-\frac{(y-1{)}^2}{9}=1$
$\therefore$ Centre is $(-1,1)$
$\Rightarrow$ Length of transverse axis = $2a=2\times 4=8$ units
$\Rightarrow$ Length of conjugate axis $=2b=2\times 3=6$ units
$\Rightarrow e^2=1+\frac{b^2}{a^2}=\frac{25}{16}$
$\therefore e=\frac{5}{4}$