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]
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Is line y = kx + b tangent to circle x^2 + y^2 = 1?
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Global Stats
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.
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.
