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Fizzle
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#1
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#1
A circle C has centre (3,2) and radius 3√2. A straight line lx has equation y=x+5. (a) Write down an equation of the circle C. (b) Calculate the exact coordinates of the two points where the line lx intersects C, giving your answer in surds. (c) Find the distance between these two points.

I understand part a.. (x-3)^2 + (y-2)^2 = 13 (IS THAT RIGHT?)
but im stuck from there.. u need to use SIMULTANEOUS EQUATIONS for part b.. can anyone plz help???
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Christophicus
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#2
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(Original post by Fizzle)
A circle C has centre (3,2) and radius 3√2. A straight line lx has equation y=x+5. (a) Write down an equation of the circle C. (b) Calculate the exact coordinates of the two points where the line lx intersects C, giving your answer in surds. (c) Find the distance between these two points.

I understand part a.. (x-3)^2 + (y-2)^2 = 13 (IS THAT RIGHT?)
but im stuck from there.. u need to use SIMULTANEOUS EQUATIONS for part b.. can anyone plz help???
a) Equation of circle
(y-b)^2 + (x-a)^2 = r^2
(a,b) are the coordinates of a circle

Therefore;
(y-2)^2 + (x-3)^2 = (3root2)^2
(y-2)^2 + (x-3)^2 = 9*2 = 18 not 13

b) Substitute y = x + 5 into circle equation.
(y-2)^2 + (x-3)^2 = 18
(x+5-2)^2 + (x-3)^2 = 18
(x+3)^2 + (x-3)^2 = 18
x^2 + 6x + 9 + x^2 - 6x + 9 - 18 = 0
2x^2 = 0
x = 0 for both points
Sub these two values into y = x + 5

Point of intersection is;
(0,5)

Either my working is incorrect or the question is flawed or you have typed it wrong. Can someone else check?
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Fizzle
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thanks so much, that really helped! x
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Christophicus
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(Original post by Fizzle)
thanks so much, that really helped! x
is this from the c2 book?
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Fizzle
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#5
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x^2 + 6x + 9 + x^2 - 6x + 9 - 18 = 0

why is it + 6x???? and - 6x?????
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Gaz031
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(Original post by Fizzle)
x^2 + 6x + 9 + x^2 - 6x + 9 - 18 = 0

why is it + 6x???? and - 6x?????
Because you multiply the 3 by the x twice and the -3 by the x twice.
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Fizzle
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oh i get it now..
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Christophicus
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Either my working is incorrect or the question is flawed or you have typed it wrong. Can someone else check?

There is only one point of intersection when there should be two.
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