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(A) The line $ax+by-1=0$ is a tangent to the circle $x^2+y^2-r^2=0$ with center $(0,0)$ and radius $r$.The perpendicular distance from the center $(0,

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$(a, b)$ lies on the circle $S_1=0$

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(A) The line $ax+by-1=0$ is a tangent to the circle $x^2+y^2-r^2=0$ with center $(0,0)$ and radius $r$.The perpendicular distance from the center $(0,0)$ to the line $ax+by-1=0$ must be equal to the radius $r$.So,$\frac{|a(0)+b(0)-1|}{\sqrt{a^2+b^2}} = r$.$\frac{1}{\sqrt{a^2+b^2}} = r$.Squaring both sides,we get $\frac{1}{a^2+b^2} = r^2$,which implies $a^2+b^2 = \frac{1}{r^2}$.If $r=1$,then $a^2+b^2 = 1$,which means the point $(a,b)$ lies on the circle $x^2+y^2=1$,i.e.,$S_1=0$.

If the line $ax+by=1$ is a tangent to the circle $S_r \equiv x^2+y^2-r^2=0$,then which one of the following is true?

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