Question

Which of the following is true regarding hyperbola $\frac{y^2}{b^2}-\frac{x^2}{a^2}=1?$

• A. $y$-axis is transverse axis.
• B. The given hyperbola do not intersect the x-axis
• C. All of the above
• D. Vertices are $(0,b)\text{and}(0,-b)$

Answer 1

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

Vertices are $(0,b)\text{and}(0,-b)$


Standard hyperbola: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$


Conjugate hyperbola: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$
Vertices are $(0,b)\text{and}(0,-b)$

For intersection with x-axis, put $y=0\Rightarrow \frac{x^2}{a^2}=-1$, which do not give any real value of $x.$
Hence, the given hyperbola do not intersect the x -axis.

Transverse axis of given hyperbola is y-axis as shown in diagram also.