Q86 / 200 · AP EAMCET 2002 · Mathematics

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

  • A
    a parabola
  • B
    an ellipse
  • Correct answer
    C
    a hyperbola
  • D
    a rectangular hyperbola

Solution

We have, $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta$ $$ \begin{array}{ccrl} \Rightarrow & & 8=r+3 r \cos \theta \\ \Rightarrow & r & =8-3 x \\ \Rightarrow & r^2 & =(8-3 x)^2 \\ \Rightarrow & & x^2+y^2=64+9 x^2-48 x \\ \Rightarrow & & 8 x^2-y^2-48 x+64=0 \end{array} $$ Which represents a hyperbola.

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

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