Q13 of 153 Page 14

If |z – 5i| = |z + 5i|, then find the locus of z.

z = a + ib


|a+ib-5i| = |a+ib+5i|


|a+ib-5i|2 = |a+ib+5i|2


|a +i(b-5)|2 = |a + i(b+5)|2


a2+(b-5)2 = a2+(b+5)2


a2+b2+25-10b = a2+b2+25+10b


20b = 0


b = 0


b is a imaginary part of z



= y


= 0


Im (z) = 0


So, the locus point is real axis


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