Find the polar of the point (4, - 1) with respect to the circle $2 x^{2} + 2 y^{2} = 11 .$

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Solution

Polar of the point $(x_{1}, y_{1})$ with respect to the circle $2 x^{2} + 2 y^{2} = 11$ is given by $2 x x_{1} + 2 y y_{1} = 11$
Substituting the point $(4, - 1)$ into the equation will give $2 x (4) + 2 y (- 1) = 11$
i.e. $8 x - 2 y = 11$ is the required polar.

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