The equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta$ represents
The equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} \cos \theta$ represents
- a parabola
- an ellipse
- a hyperbola
- 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
Asked in: AP EAMCET 2002
Practice more Ellipse questions on Aicharya