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  • The radical centre of circles represented by  <img alt="\mathrm{\begin{aligned} & S_1: x^2+y^2-7 x-6 y-4=0 \\ & S_2+x^2+y^2-8 x-4 y-4=0 \end{aligned}}" src="https://entrancec

The radical centre of circles represented by 

\mathrm{\begin{aligned} & S_1: x^2+y^2-7 x-6 y-4=0 \\ & S_2+x^2+y^2-8 x-4 y-4=0 \end{aligned}}

And \mathrm{\begin{aligned} S_1: x^2+y^2+10 x+6 y-4=0 \end{aligned}} is given by

Option: 1

(-1,1)


Option: 2

(1,-1)


Option: 3

(0,0)


Option: 4

None of these 


Answers (1)

best_answer

Radical axis of two circles is a line perpendicular
to the line joining the centres of given circles where as
radical centre of three circles is the point of concurrency
of radical axis of three circles when two circles are taken
at a time.
Now, radical axis of circles

\mathrm{\begin{aligned} & S_1: x^2+y^2-7 x-6 y-4=0 \\ & S_3: x^2+y^2+10 x+6 y-4=0 \\ & S_1-S_3=0 \Rightarrow 17 x+12 y=0 \end{aligned}}

Similarly, radical axis of \mathrm{S_{1}} and \mathrm{S_{2}} is \mathrm{S_1-S_2=0 \Rightarrow x-2 y=0}

and that of \mathrm{S_{2}} and \mathrm{S_{3}} is \mathrm{9x+5y=0}.Now, equations of there radical axis are \mathrm{17 x+12 y=0, x-2 y=0,9 x+5 y=0} and
point of intersection of each pair of radical axis is origin.
∴ Radical centre = (0, 0)

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