The chord of least length which passes through the point $(2, 1)$ of the circle $x^{2} + y^{2} - 2 x - 4 y - 13 = 0$ is

2

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3 \sqrt{2}

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2 \sqrt{3}

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8

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Solution

The correct option is D $8$
Shortest chord passing through P (x,y) is a chord whose mid-point is
P(n,y)
for least chord AB, P must be mid-point of AB In $△ O P A$
$O P^{2} + P A^{2} = O A^{2}$
$2 + P A^{2} = (\sqrt{16})^{2}$
$P A^{2} = 16$
$P A = 4$
then length of a shortest chord is 8

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The chord of least length which passes through the point (2,1) of the circle x2+y2−2x−4y−13=0 is

The correct option is D 8Shortest chord passing through P (x,y) is a chord whose mid-point isP(n,y)for least chord AB, P must be mid-point of AB In △ OPAOP2+PA2=OA22+PA2=(√16)2PA2=16PA=4then length of a shortest chord is 8

The chord of least length which passes through the point $(2, 1)$ of the circle $x^{2} + y^{2} - 2 x - 4 y - 13 = 0$ is

The correct option is D $8$
Shortest chord passing through P (x,y) is a chord whose mid-point is
P(n,y)
for least chord AB, P must be mid-point of AB In $△ O P A$
$O P^{2} + P A^{2} = O A^{2}$
$2 + P A^{2} = (\sqrt{16})^{2}$
$P A^{2} = 16$
$P A = 4$
then length of a shortest chord is 8