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Beyond Horizon Set 2 Paper 1 · Q5

Paper 1GeometryAlgebra

Find the complete set of values of pp for which the equation

x2−3px+y2−4y−p2+6p+7=0x^2-3px+y^2-4y-p^2+6p+7=0

describes a circle in the xyxy-plane.

Ap<−73p<-\frac73
Bp<12−10513p<\dfrac{12-10\sqrt5}{13} or p>12+10513p>\dfrac{12+10\sqrt5}{13}
Cp<10−10313p<\dfrac{10-10\sqrt3}{13} or p>10+10313p>\dfrac{10+10\sqrt3}{13}
Dp<12−10313p<\dfrac{12-10\sqrt3}{13} or p>12+10313p>\dfrac{12+10\sqrt3}{13}
Ep<−2p<-2 or p>8p>8
FAll real values of pp

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