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Official 2021 Paper 2 · Q15

Paper 2Logic & proofGeometryAlgebra

A circle has equation

x2+ax+y2+by+c=0x^2+ax+y^2+by+c=0

where aa, bb and cc are non-zero real constants.

Which one of the following is a necessary and sufficient condition for the circle to be tangent to the yy-axis?

Aa2=4ca^2=4c
Bb2=4cb^2=4c
Ca2=a2+b24−c\displaystyle\frac a2=\sqrt{\frac{a^2+b^2}4-c}
Db2=a2+b24−c\displaystyle\frac b2=\sqrt{\frac{a^2+b^2}4-c}
E−a2=a2+b24−c\displaystyle-\frac a2=\sqrt{\frac{a^2+b^2}4-c}
F−b2=a2+b24−c\displaystyle-\frac b2=\sqrt{\frac{a^2+b^2}4-c}

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