AP EAMCET · Maths · Ellipse
The equation \(\frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta\) represents
- A a parabola
- B an ellipse
- C a hyperbola
- D a rectangular hyperbola
Answer & Solution
Correct Answer
(C) a hyperbola
Step-by-step Solution
Detailed explanation
We have, \(\frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta\) \[ \begin{array}{ccrl} \Rightarrow & & 8=r+3 r \cos \theta \\ \Rightarrow & r & =8-3 x \\ \Rightarrow & r^2 & =(8-3 x)^2 \\ \Rightarrow & & x^2+y^2=64+9 x^2-48 x \\ \Rightarrow & & 8 x^2-y^2-48 x+64=0 \end{array} \]…
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