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Circles

4 A circle with centre C has equation x2+y2+2x-12y+12


2

(c) Show that the circle does not intersect the x-axis.
(d) The line with equation x+y=4 intersects the circle at the points P and Q.
(i) Show that the x-coordinates of P and Q satisfy the equation
x2+3x-10=0
(ii) Given that P has coordinates (2, 2), find the coordinates of Q.
(iii) Hence find the coordinates of the midpoint of PQ
this is the last part of c1 i have any trouble with could someone tell me how to do each of these parts much apreciated :smile:
Original post by Ganhad
4 A circle with centre C has equation x2+y2+2x-12y+12


2

(c) Show that the circle does not intersect the x-axis.
(d) The line with equation x+y=4 intersects the circle at the points P and Q.
(i) Show that the x-coordinates of P and Q satisfy the equation
x2+3x-10=0
(ii) Given that P has coordinates (2, 2), find the coordinates of Q.
(iii) Hence find the coordinates of the midpoint of PQ
this is the last part of c1 i have any trouble with could someone tell me how to do each of these parts much apreciated :smile:


First put x2 + y2 + 2x - 12y + 12 into (x-a)2 + (y-b)2 = r2.

What is the equation of the x-axis?
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Ganhad
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x2+2x+12?
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Ganhad
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Original post by thegodofgod
First put x2 + y2 + 2x - 12y + 12 into (x-a)2 + (y-b)2 = r2.

What is the equation of the x-axis?


x2+2x+12?
Original post by Ganhad
x2+2x+12?


x2 + y2 + 2x - 12y + 12 = 0

x2 + 2x + y2 - 12y = - 12

(x + 1)2 - 1 + (y - 6)2 - 36 = - 12

(x + 1)2 + (y - 6)2 = - 12 + 1 + 36

(x + 1)2 + (y - 6)2 = 25

(x + 1)2 + (y - 6)2 = 52

This tells you that the centre of the circle is (-1, 6) and the radius is 5.

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