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TS EAMCET · Maths · Ellipse

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

  1. A a parabola
  2. B an ellipse
  3. C a hyperbola
  4. D a rectangular hyperbola
Verified Solution

Answer & Solution

Correct Answer

(C) a hyperbola

Step-by-step Solution

Detailed explanation

We have, \(\frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta\) \[ \begin{array}{ccrl} \Rightarrow & & 8=r+3 r \cos \theta \\ \Rightarrow & r & =8-3 x \\ \Rightarrow & r^2 & =(8-3 x)^2 \\ \Rightarrow & & x^2+y^2=64+9 x^2-48 x \\ \Rightarrow & & 8 x^2-y^2-48 x+64=0 \end{array} \]…