if a circle passes through the point of intersection of the co-ordinate axes with the lines kx-y+1=0 and x-2y+3=0. find k.
Notice that kx - y + 1 = 0 and x - 2y + 3 = 0 have different y intercepts because
y = kx -1 for the first line and
y = 1/2x - 3/2 for the second line
Therefore they can only intersect the coordinate axes on the X axis. That is where the x - intercept is.
The x - intercept is found where y = 0
Therefore, for the first second line:
0 = 1/2x -3/2
1/2x = 3/2
x = 3
The first line MUST have the same x - intercept, so we plug in x = 3 and solve for k:
0 = kx - 1
0 = k(3) -1
3k = 1
k = 1/3
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