Is line y = kx + b tangent to circle x^2 + y^2 = 1?

[VJesus12]

Is line y = kx + b tangent to circle x^2 + y^2 = 1 ?

(1) k + b = 1
(2) k^2 + b^2 = 1

[spoiler]OA=E[/spoiler]

Source: GMAT Club Tests

[swerve]

Rephrasing the question, we have

What are the values of variables \(k\) and \(b\)?

1. Insufficient. The sum is not enough
2. Insufficient. The sum of squares is not enough.

Combine \(1)\) and \(2)\)

\(k^2 + b^2 = 1 \quad\cdots\quad(1)\)

And

\(k + b = 1\)

Square both sides

\(k^2 + b^2 + 2kb = 1 \quad\cdots\quad(2)\)

Hence \(2kb = 0\).

Either \(k = 0\) or \(b = 0\). We are not sure. There is no way to determine the values of \(k\) and \(b\).

Therefore, __E__ is the correct option.