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Choosing a given statement is true/false.

The pole of the straight line 2x-y=1 with respect to the circle $5 x^{2} + 5 y^{2} = 9$ is $(\frac{- 18}{5}, \frac{9}{5})$ .

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True

False

answer is B.

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Detailed Solution

Let us first assume the pole of this line to be (h,k).
We know that the polar line is given by using T=0.
The equation of the polar line when the pole is (h,k) is given as:
T=0
⇒5x.h+5.y.k=9
⇒5hx+5ky=9
The given polar line to us is 2x−y=1.

\Rightarrow \frac{5 h}{2} = \frac{5 k}{- 1} = \frac{9}{1}

\Rightarrow h = \frac{18}{5}, k = \frac{- 9}{5}

Thus, the required pole of this line is

(\frac{18}{5}, \frac{- 9}{5})

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