Q46 / 120 · VITEEE 2017 · Mathematics

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

  • A
    A rectangular hyperbola
  • Correct answer
    B
    A hyperbola
  • C
    An ellipse
  • D
    A parabola

Solution

Given, equation is $$ \frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta \text { or } \frac{8}{\mathrm{r}}=1+3 \cos \theta $$ which is the form of $\frac{l}{r}=1+e \cos \theta$ $$ \because \quad e=3>0 $$ $\therefore \quad$ Given equation is a hyperbola.

Hence, the correct answer is option: 'B'.

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