Find the equation of circle whose centre is (3,-1) and which cut off an intercept of length 6 units from the line 2x-5y+18=0.

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Please find below the solution to the asked query:

We have, centre of circle Ch,k = C3,-1 equation of chord , AB=2x-5y+18Now, we drop a perpendicular CM on the chord, CM=2.3-5.-1+1822+-52=2929=29 unitsMB=3 units  drawn from the centre to the chord bisects the chordIn CMB, CB2=CM2+MB2   Pythagoras TheoremCB2=292+32CB2=29+9=38CB=38unitsr=CBhence equation of circle:x-h2 + y-k2 = r2x-32+y+12=38

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