Question

What will be the parametric equation of tangent at the point $P(8\sec \theta ,8\tan \theta )$ on a rectangular hyperbola
$x^2-y^2=a^2?$

• A. $x\sec \theta -y\tan \theta =64$
• B. $x\sec \theta -y\tan \theta =8$
• C. $x\tan \theta -y\sec \theta =8$
• D. $x\sec \theta +y\tan \theta =8$

Answer 1

The correct option is B $x\sec \theta -y\tan \theta =8$

Given: Point $P(8\sec \theta ,8\tan \theta )$

To Find: Parametric equation of tangent

We know that the equation of tangent at $P(a\sec \theta ,a\tan \theta )$ on rectangular hyperbola is: $x\sec \theta -y\tan \theta =a$

From the given data, we have $a=8$

Substituting all the values in the equation of tangent.
$x\sec \theta -y\tan \theta =8$