標題:
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Coordinate Treatment of Simple Locus Problems
發問:
A straight line L intersects the x-axis and the y-axis at points A and B respectively such that AB = 10. Find a possible equation of straight line L.
最佳解答:
Let A be ( x , 0 ) and B be ( 0 , y ). For AB = 10, √[ ( x - 0 )^2 + ( 0 - y )^2 ] = 10 x^2 + y^2 = 100 For the values of x and y, it is simpler to consider them as intergers as the Q just asks for a possible equation of L. Then x and y may have the following possibilities (choose 1 of them as the answer): ( 1 ) x = 6, y = 8 L: ( 0 - 8 ) / ( 6 - 0 ) = ( y - 0 ) / ( x - 6 ) 4x + 3y - 24 = 0 ( 2 ) x = 8, y = 6 L: ( 6 - 0 ) / ( 0 - 8 ) = ( y - 6 ) / ( x - 0 ) 3x + 4y - 24 = 0 ( 3 ) x = -6, y = 8 L: ( 0 - 8 ) / ( - 6 - 0 ) = ( y - 0 ) / ( x + 6 ) 4x - 3y + 24 = 0 ( 4 ) x = -6, y = -8 L: ( 0 + 8 ) / ( - 6 - 0 ) = ( y - 0 ) / ( x + 6 ) 4x + 3y + 24 = 0 ( 5 ) x = -8, y = 6 L: ( 0 - 6 ) / ( - 8 - 0 ) = ( y - 0 ) / ( x + 8 ) 3x - 4y + 24 = 0 ( 6 ) x = -8, y = -6 L: ( y + 6 ) / ( x - 0 ) = ( -6 - 0 ) / ( 0 + 8 ) 3x + 4y + 24 = 0 ( 7 ) x = 6, y = -8 L: ( 0 + 8 ) / ( 6 - 0 ) = ( y - 0 ) / ( x - 6 ) 4x - 3y - 24 = 0 ( 8 ) x = 8, y = - 6 L: ( 0 + 6 ) / ( 8 - 0 ) = ( y - 0 ) / ( x - 8 ) 3x - 4y - 24 = 0
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