Question

Select the right options about a hyperbola.

• A. Conjugate axis is the axis of the hyperbola that passes through the foci
• B. A transverse axis always pass through the origin
• C. The straight line through the centre which is perpendicular to the transverse axis doesn't meet hyperbola in real point.
• D. Eccentricity is the ratio of 2 distances

Answer 1

Answer: (C), (D)

The correct options are
C

The straight line through the centre which is perpendicular to the transverse axis doesn't meet hyperbola in real point.

D

Eccentricity is the ratio of 2 distances

These are some basic facts associated with the hyperbola.

Eccentricity is the ratio of distances between a point p from the curve to a fixed between and between p and a fixed line.

Also, conjugate axis doesn't meet the hyperbola in real points, while transverse axis meets the curve at 2 points.

Here in the given hyperbola

$x^{1}ox\to$ Transverse axis

$y^{1}oy\to$ conjugate axis

Eccentricity$=e=\frac{PS}{PQ}$