Oxford University MAT 2016 Solved Papers

Question : 3 of 10

Marks: +1, -0

The origin lies inside the circle with equation

x^2+a x+y^2+b y=c

precisely when

Solution:

C. We can rewrite the given equation as

(x+\;{a}/{2})^2+(y+\;{b}/{2})^2=c+\;{a^2}/{4}+\;{b^2}/{4}

. For the circle to contain the origin, the distance from the centre to the origin must be less than the radius, so

\;{a^2}/{4}+\;{b^2}/{4}< c+\;{a^2}/{4}+\;{b^2}/{4}

. The answer is (a).

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