The polar equation cos θ+7 sin θ=1/r represents a

Correct answer: (C) straight line. Polar equation is cos θ+7 sin θ=1/r ⇒ r cos θ+7 r sin θ=1 Put x=r cos θ, y=r sin θ , we get ⇒ x+7 y=1 This is the equation of straight line.

Q99 / 160 · TS EAMCET 2004 · Mathematics

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

A
circle
B
parabola
Correct answer
C
straight line
D
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.

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

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