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JEE Advanced Model Paper 11 with solutions for online practice

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Question : 51

Total: 60

Consider the hyperbola H : x2−y2 = 0 and a circle S with centre C (α, 0).Suppose H and S touch each other at P (θ , Φ) with ϕ > 1 and Φ > 0 . The commontangent to H and S at P intersects the x-axis at point Q. If (β , r) is centroid ofΔPQC then the correct expression (s) among the following is ( are) _________

dβ
dθ
= 1 -
1
3θ2
; θ > 1
dr
dθ
=
θ
3√θ2−1
; θ > 1
dβ
dθ
= 1 +
1
3θ2
; θ > 1
dr
dΦ
=
1
3
; Φ > 0

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