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  • If (a, b) is a common point of the two circles <img alt="\mathrm{x^2+y^2-6 x-9 y+13=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2-6%20x-9%20y&plus;13

If (a, b) is a common point of the two circles \mathrm{x^2+y^2-6 x-9 y+13=0} and \mathrm{x^2+y^2-2 x-16 y=0}, then a+b=

Option: 1

6


Option: 2

4


Option: 3

8


Option: 4

2


Answers (1)

best_answer

\mathrm{\text { The common chord of the circles is } S-S^{\prime}=0}

\mathrm{\Rightarrow 4 x-7 y=13}       ...[i]

Eliminating x between the second circle and the line (i), we get

\mathrm{\begin{aligned} & y^2-2 y+1=0 \Rightarrow y=1, x=5 \\ & \therefore \quad a=5, b=1, a+b=6 . \end{aligned}}

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