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Find the equation of the locus when the distance of P from the line x=4 is equal to its distance from the line y = 1
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The locus for is the straight line passing through the point (x,y) = (4,1) and having the slope 1:
y - 1 = x - 4, or y = x - 3.
Make a sketch. Draw the coordinate axes. Draw the line x = 4 and the line y = 1. Then draw your line.