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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Apr 14, 2019 10:19 am

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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

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 14, 2019 10:19 am

swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Apr 14, 2019 2:35 pm

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.

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