Question 792785: Determine if the circles defined by each pair of equations intersect
a)x^2 + y^2 - 10x + 2y + 17 = 0 , x^2 + y^2 + 6x + 14y + 9 = 0
b)x^2 + y^2 - 4x + 6y + 9 = 0 , x^2 + y^2 - 2x - 4y - 8 = 0
Can you please help me out? Thank you so much in advance:)
Can you also please show the steps it would really help me understand better:)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Determine if the circles defined by each pair of equations intersect
a)x^2 + y^2 - 10x + 2y + 17 = 0 , x^2 + y^2 + 6x + 14y + 9 = 0
Find the center and the radius of each circle.
Put the equations in standard form by completing the squares.
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x^2 + y^2 - 10x + 2y + 17 = 0
x^2 - 10x + y^2+ 2y = -17
x^2-10x+25 + y^2+2y+1 = -17 + 25 + 1 = 9
(x-5)^2 + (y+1)^2 = 3^2
--> circle of radius 3, center at (5,-1)
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x^2 + y^2 + 6x + 14y + 9 = 0
Do the 2nd eqn the same way.
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Then, if sum of the 2 radii are less than the distance between the 2 centers, they don't intersect.
If it's equal, they're tangent, 1 intersection
It the sum is greater than the distance, there are 2 intersections.
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Email via the TY note for help, or to check your work.
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dl the FREE graph software at
http://www.padowan.dk
to graph them.
Use F6 to enter them as they are.
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b)x^2 + y^2 - 4x + 6y + 9 = 0 , x^2 + y^2 - 2x - 4y - 8 = 0
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