The number points on the circle $x^{2} + y^{2} - 4 x - 10 y + 13 = 0$ which are at distance $1$ from the point $(- 3, 2)$ is

1

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2

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3

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None of these

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Solution

The correct option is B None of these
Given circle is
$x^{2} + y^{2} - 4 x - 10 y + 13 = 0$
Its centre is $C \equiv (2, 5)$ and radius $= 4$
Also, $A C = \sqrt{{(2 - 5)}^{2} + {(- 3 - 2)}^{2}} = \sqrt{9 + 25} = \sqrt{34} = 5.83.$
$∴ A B = A C - B C = 5, 83 - 4 = 1.83 > 1.$
$∴$ There is no point on the circle at a distance $1$ from the point $(- 3, 2) .$

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