C2 2017 5 Edexcel

5

a) x^2 +y^2 -10x+6y+30
= (x-5)^2 -25 + (y+3)^2 -9 +30
=(x-5)^2 + (y+3)^2-4
\therefore equation of the circle is: (x-5)^2 + (y+3)^2=4
Centre = (5,-3)

b) radius=2

c) substituting x=4 into the circle equation gives
1+(y+3)^2=4
(y+3)^2=3
y=-3\pm \sqrt{3}

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:handshake: :handshake:

5(a) The equation of C can be rewritten as (x-5)^2 + (y+3)^2 = 4
Hence its centre is (5,-3)

(b) The radius of C is sqrt (4) =2 (I don’t understand why this is worth 2 marks, should be only 1)

© When x=4, 1+ (y+3)^2 =4 so (y+3)^2 = 3, y+3 = ±sqrt(3) so y= ±sqrt (3) -3

This is more like a 5 mark question

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:+1: :+1: @q00 :+1: :+1: