If the coordinates of a point be given by the equations x = b , ;… - Vidyadip

MCQ

If the coordinates of a point be given by the equations $x = b\sec \phi ,\;\;y = a\tan \phi $, then its locus is

A
A straight line
B
A circle
C
An ellipse
✓
A hyperbola

✓

Answer

Correct option: D.

A hyperbola

d
(d) Here $\frac{x}{b} = \sec \phi $ and $\frac{y}{a} = \tan \phi $

Therefore $\frac{{{x^2}}}{{{b^2}}} - \frac{{{y^2}}}{{{a^2}}} = {\sec ^2}\phi - {\tan ^2}\phi \,\,$

$\Rightarrow \,\,\frac{{{x^2}}}{{{b^2}}} - \frac{{{y^2}}}{{{a^2}}} = 1$,

which is obviously a hyperbola.

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