Geometry

Find the points of intersection of the line X+Y=5, and the circle x^2+y^2=25 by solving the system of equations.

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  1. well, y = 5-x, so

    x^2 + (5-x)^2 = 25

    now just expand and solve the quadratic.

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  2. x+5/30=4x-10/75

    2*3*5*5*(x+5)/2*3*5=2*3*5*5(4x-10)/3*5*5

    5*(x+5)=2*(4x-10)
    5x+25=8x-20
    25+20=3x
    3x=45
    x=15

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  3. x=0, y=0
    x=5,y=25
    no other solutions

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  4. The x=15 is ok

    Not sure what the last set of values is for, but if they are for the 1st problem, no good.

    x^2 + (5-x)^2 = 25
    x^2 + x^2-10x+25 = 25
    2x^2-10x = 0
    2x(x-5) = 0

    x = 0 or x=5

    So, the points of intersection are (0,5) and (5,0)

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