circles part b ..help ! 2nd

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maths_arghh234

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hii again :) ...the circle x^2 +y^2+4x -16y +18 =0 has a centre A and radius r

a ) find the coordinates of A and the value of r ......A (-2,8) r=2

b) the line y= x+2 and the circle x^2 +y^2 +4x -16 y+18 =0 intersect at the points B and C Find the coordinates of B and C...

please help me with part b .. i thought maybe you use a simultaneous equations method somehow but i expect i'm wrong ...:\ lol
 
maths_arghh234 said:
hii again :) ...the circle x^2 +y^2+4x -16y +18 =0 has a centre A and radius r

a ) find the coordinates of A and the value of r ......A (-2,8) r=2

b) the line y= x+2 and the circle x^2 +y^2 +4x -16 y+18 =0 intersect at the points B and C Find the coordinates of B and C...

please help me with part b .. i thought maybe you use a simultaneous equations method somehow but i expect i'm wrong ...:\ lol
Click to expand...

y = x + 2 ....................................(1)

x^2 +y^2 +4x -16 y+18 =0 ...............(2)

Replace 'y' in (2) by 'x + 2' [from (1)]

x^2 +(x+2)^2 +4x -16 (x+2)+18 =0 ......................(3)

Expand (3) and you'll get a quadratic equation in "x".

Solve for x - you'll get two values of 'x'. Those are the 'x-coordinates' of the points of intersections.

Use those in equation in (1) - to get two values of the 'y' co-ordinates.
 
thanks !!
Subhotosh Khan said:
xpand (3) and you'll get a quadratic equation in "x".
Click to expand...
i tried it and came up with 2x^2-10x -10 = 0 ... but i'm having trouble factorising it :S
 
maths_arghh234 said:
thanks !!
[quote="Subhotosh Khan":3oarn2am]xpand (3) and you'll get a quadratic equation in "x".
Click to expand...
i tried it and came up with 2x^2-10x -10 = 0 ... but i'm having trouble factorising it :S[/quote:3oarn2am]

How did you get that? - Please show work.
 
sorry ...
sub y=x+2 into x^2+y^2+4x-16y+18 =0 ....

x^2 +(x+2)^2+4x-16(x+2)+18=0
expand x^2+ x^2+2x+4+4x -16x -32 +18 =0
2x^2-10x-10=0
 
maths_arghh234 said:
sorry ...
sub y=x+2 into x^2+y^2+4x-16y+18 =0 ....

x^2 +(x+2)^2+4x-16(x+2)+18=0
expand x^2+ x^2+2x+4+4x -16x -32 +18 =0<<<< That should be 4x
2x^2-10x-10=0
Click to expand...
 
maths_arghh234 said:
aaaahhhhh ....okay so does this make more sense... 2x^2-8x-10 :?:
Click to expand...

Yes - now factorize - that should be relatively simple.
 
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