First slide

Equation of line in Straight lines

Question

If the distance of any point P(x, y) from the origin is defined as d(x, y) = Max. $(| x |, | y |)$ and d(x, y) = a (non zero constant), then the locus of the P is

Moderate

A

Square
B

Triangle
C

Straight line
D

Pair of lines

Solution

d(x, y) = Max. $(| x |, | y |)$ .....(i)
But d(x, y) = a ..... (ii)
From (i) and (ii),
a = Max.
If |x| > |y|, then a = |x| x = ± a
If |y| > |x|, then a = |y| y = ± a
Hence locus of P represents a square

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