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Euclid Sample Paper 1 · Q19

Paper 1Geometry

For a real parameter pp, consider the two curves

Cp:(∣x∣−1)2+y2=(p+1)2C_p:\quad (|x|-1)^2+y^2=(p+1)^2

and

Dp:x2+(∣y∣−1)2=(p+1)2.D_p:\quad x^2+(|y|-1)^2=(p+1)^2.

The curves intersect at eight distinct points. The four intersection points nearest the origin are the vertices of a square SS, while the other four are the vertices of a square TT. It is given that

Area⁡(T)=9Area⁡(S).\operatorname{Area}(T)=9\operatorname{Area}(S).

Find the value of p2+2pp^2+2p.

A−78-\frac78
B−58-\frac58
C−38-\frac38
D−18-\frac18
E18\frac18
F38\frac38
G58\frac58
H78\frac78

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