M17 #12

The circle represented by the equation \(x^2+y^2 = 1\) is centered at the origin and has the radius of \(r=\sqrt{1}=1\) (for more on this check Coordinate Geometry chapter of math book: math-coordinate-geometry-87652.html ).

(1) K + B = 1 --> if \(k=0\) and \(b=1\) then the equation of the line becomes \(y=1\) and this line is tangent to the circle but if \(k=1\) and \(b=0\) then th equation of the line becomes \(y=x\) and this line is NOT tangent to the circle. Not sufficient.

(2) K^2 + B^2 = 1. The same example is valid for this statement too. Not sufficient.

(1)+(2) Again the same example satisfies both statement: if \(k=0\) and \(b=1\) then the equation of the line becomes \(y=1\) and this line is tangent to the circle but if \(k=1\) and \(b=0\) then th equation of the line becomes \(y=x\) and this line is NOT tangent to the circle. Not sufficient.

Answer: E.