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Condition for Two Lines to Be Perpendicular

What loci are...

Question

What loci are represented by the equations :
$(x - a)^{2} - y^{2} = 0 .$

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Solution

${(x - a)}^{2} - y^{2} = 0$
Factorising the given equation
$(x - a + y) (x - a - y) = 0 x + y - a = 0, x - y - a = 0$
Slope of first line $= - 1$
Slope of second line $= 1$
Product of slopes $= - 1$
Hence the equation represents a pair of perpendicular straight lines.

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