Question

The lengths of the transverse axis and the conjugate axis of the hyperbola $9x^2-y^2=1$ are and respectively.

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

Answer 1

Answer: (A), (C)

The correct options are
A $2$
C $\frac{2}{3}$

$\mathrm{The}\mathrm{equation}9x^2-y^2=1\mathrm{can}\mathrm{be}\mathrm{written}\mathrm{as}\frac{x^2}{\left(\frac{1}{9}\right)}-\frac{y^2}{1}=1\mathrm{This}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\therefore a^2=\frac{1}{9},b^2=1\Rightarrow a=\frac{1}{3},b=1\therefore \mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{conjugate}\mathrm{axis}=2b=2\mathrm{and}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{transverse}\mathrm{axis}=2a=\frac{2}{3}$