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Clavis TMUA Set A Paper 1 · Q3

Paper 1Algebra

The circles C1C_1 and C2C_2 have equations

C1:x2+y2=25C2:(x−a)2+(y−a)2=9C_1:x^2+y^2=25\qquad C_2:(x-a)^2+(y-a)^2=9

where aa is a real constant.

Find the complete set of values of aa for which C1C_1 and C2C_2 intersect at two distinct points.

A−42<a<42-4\sqrt2<a<4\sqrt2
B−8<a<−2-8<a<-2 or 2<a<82<a<8
C−42<a<−2-4\sqrt2<a<-\sqrt2 or 2<a<42\sqrt2<a<4\sqrt2
D−2<a<2-\sqrt2<a<\sqrt2
E2<a<42\sqrt2<a<4\sqrt2
Fa<−42a<-4\sqrt2 or a>42a>4\sqrt2

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