Question 672786: The circle (x – 4)2 + (y – 3)2 = 4 has centre C and radius r.
The line y = x + 1 intersects this circle at two points A and B.
Find the coordinates of A and B.
Some working out would be appreciated to learn for next time :D
Thanks in advance
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The circle (x – 4)2 + (y – 3)2 = 4 has centre C and radius r.
The line y = x + 1 intersects this circle at two points A and B.
Find the coordinates of A and B.
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Substitute for "y" and solve for "x":
(x-4)^2 + (x+1-3)^2 = 4
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x^2 -8x +16 + (x^2-4x+4) = 4
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2x^2 -12x +16 = 0
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x^2 -6x +8 = 0
Factor:
(x-4)(x-2) = 0
x = 2 or x = 4
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Solve for the corresponding "y": values using y = x+1
If x = 2, y = 3
If x = 4, y = 5
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Points of intersection: (2,3) and (4,5)
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Cheers,
Stan H.
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