Question

For hyperbola $-\frac{(x-1{)}^2}{3}+\frac{(y+2{)}^2}{16}=1$ distance between directrices is ?

• A. $\frac{2}{\sqrt{19}}$
• B. $\frac{3}{\sqrt{19}}$
• C. $\frac{4}{\sqrt{19}}$
• D. $\frac{32}{\sqrt{19}}$

Answer 1

Answer: (D)

$\frac{32}{\sqrt{19}}$

Comparing the equation of given hyperbola with the standard equation

$\frac{(y-k{)}^2}{a^2}-\frac{(x-h{)}^2}{b^2}=1$

$h=1,k=-2,a^2=16,b^2=3$

$e=\sqrt{1+\frac{b^2}{a^2}}=\frac{\sqrt{19}}{4}$

Distance between the directrices $=\frac{2a}{e}=\frac{32}{\sqrt{19}}$