C2 2015 2 Edexcel

2

a) circle has centre (2,-1) so the equation is of the form (x-2)^2+(y+1)^2=r^2
We know (4,-5) satisfies this so substituting this gives us r^2=20
\therefore equation is (x-2)^2+(y+1)^2=20

b) x^2-4x+4+y^2+2y+1=20
By implicit differentiation we have
2x-4+\frac{\mathrm{d} }{\mathrm{d} x}2y+ \frac{\mathrm{d} }{\mathrm{d} x}2=0
\frac{\mathrm{d} }{\mathrm{d} x}=\frac{2-x}{y+2}
At A the gradient is \frac{2-4}{-5+2}=2/3
Y=2/3 X+ c
Substituting (4,-5) gives c=-23/3
\therefore y=2/3 x -23/3
3y-2x+23=0

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