tmua.fyi Mock Paper 2 (2) · Question 4

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tmua.fyi Mock Paper 2 (2) · Q4

Paper 2Logic & proofGeometry

The line $y=mx+c$ (with $c\ne0$ ) and the circle $x^2+y^2=a^2$ (with $a>0$ ) are given. Consider statement P: ‘the line is tangent to the circle’, and statement Q: ‘ $c^2=a^2(1+m^2)$ ’. Then Q is:

Anecessary but not sufficient for P.

Bsufficient but not necessary for P.

Cboth necessary and sufficient for P.

Dneither necessary nor sufficient for P.

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