Question

Which of the following is incorrect regarding Latus rectum of a rectangular hyperbola?

• A. It is perpendicular to $y=x$
• B. There can be infinte number of focal chord and latus rectum in a hyperbola.
• C. There can be infinite number of focal chord but only two latus rectum in a hyperbola.
• D. It passes through focus.

Answer 1

The correct option is B There can be infinte number of focal chord and latus rectum in a hyperbola.

Properties of Latus rectum:
$\to$ It passes through focus.
$\to$ It is perpendicular to the transverse axis$(y=x)$
Chords passing through focus are called focal chords. And there can be infinte number of focal chords.
But, only two focal chords are possible which are perpendicular to transverse axis and passing through foci.
Hence, the correct answer is option d.