The polar equation $\cos \theta+7 \sin \theta=\frac{1}{r}$ represents a

The polar equation $\cos \theta+7 \sin \theta=\frac{1}{r}$ represents a
  1. circle
  2. parabola
  3. straight line
  4. hyperbola

Solution

Polar equation is $ \begin{aligned} & \quad \cos \theta+7 \sin \theta=\frac{1}{r} \\ & \Rightarrow r \cos \theta+7 r \sin \theta=1 \\ & \text { Put } \quad x=r \cos \theta, y=r \sin \theta \text {, we get } \\ & \Rightarrow \quad x+7 y=1 \end{aligned} $ This is the equation of straight line

Asked in: AP EAMCET 2004

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