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Question

The length of the chord AB of the circle x2+y26x+8y13=0 whose midpoint is (2,3) is (units)

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Solution

Given circle is x2+y26x+8y13=0
Length of chord with given midpoint
=2|S1|=2|4+9122413|
=2|36|=12 units


Alternate solution :
Given circle is x2+y26x+8y13=0
Centre and radius are
C=(3,4), r=38
Distance between centre and midpoint of the chord is
d=12+12=2
Length of chord
=2r2d2
=2382=12 units

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