Equation 1 r = 1 8 + 3 8 represents - Vidyadip

MCQ

Equation $\frac{1}{r} = \frac{1}{8} + \frac{3}{8}\cos \theta $ represents

A
A rectangular hyperbola
✓
A hyperbola
C
An ellipse
D
A parabola

✓

Answer

Correct option: B.

A hyperbola

b
(b) Given, equation is $\frac{1}{r} = \frac{1}{8} + \frac{3}{8}\,\cos \theta $

or $\frac{8}{r} = 1 + 3\cos \theta $

which is the form of $\frac{l}{r} = 1 + e\cos \theta $

$\because \,e = 3 > 0$,

$\therefore \,$ Given equation is a hyperbola.

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