The $(1, 1)$ lie with respect to circle $x^{2} + y^{2} - 2 x - 6 y + 7 = 0$

inside the circle

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on the circle

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out side the circle

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can not say

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Solution

The correct option is C out side the circle
Let $S (x, y) = x^{2} + y^{2} - 2 x - 6 y + 7$
$∴ S (1, 1) = 1 + 1 - 2 - 6 + 7 = 1 > 0$
Hence point $(1, 1)$ lies outside the given circle.

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