Given is the polar $4 x + y + 12 = 0$ of the parabola $y^{2} = - 4 x$ , find the coordinates of the pole.

(4, 1 / 2)

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(3, 1 / 3)

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(3, 1 / 2)

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(4, 1 / 3)

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Solution

The correct option is B $(3, 1 / 2)$
Let $(x_{1}, y_{1})$ be co-ordinates of pole
Polar is given by ${y y}_{1} = - 2 ({x + x}_{1})$
i.e. $2 x + {y y}_{1} + 2 x_{1} = 0$ .... $(i)$

Given polar is $4 x + y + 12 = 0$ ...... $(i i)$
Comparing coefficients we get

$\frac{4}{2} = \frac{1}{y_{1}} = \frac{12}{{2 x}_{1}}$

$x_{1} = 3, y_{1} = 1 / 2$

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