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tmua.me Extreme Set B Paper 2 · Q1

Paper 2Logic & proofGeometryAlgebra

The points A=(−1,0)A=(-1,0) and B=(1,0)B=(1,0) are fixed. The line LL has equation

y=mx+c,y=mx+c,

where mm and cc are real constants.

Consider the statements

  • S: c2≤m2c^2\leq m^2.
  • T: LL meets every circle through AA and BB at two distinct points.

Is S necessary and/or sufficient for T?

AS is neither necessary nor sufficient for T
BS is necessary but not sufficient for T
CS is sufficient but not necessary for T
DS is necessary and sufficient for T

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