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Question

Find the value of k, if the point (1, 3) and (2, k) are conjugate with respect to the circle $$x^2 + y^2 = 35$$.


Solution

Since points $$(1,3)$$ and $$(2,k)$$ are conjugate w.r.t. the given circle, both the points lie on the polar of the other point.
$$\therefore (1,3)$$ lies on $$x(2) + y(k) - 35 = 0$$
i.e. $$2 \times 1 + 3 \times k - 35 = 0$$
$$\therefore 3k = 33$$ or $$k = 11$$

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