Locus of the point z satisfying the equation - i z -1- z - i -2 isA- an ellipseB- a straight lineC- a pair of straight linesD- a circle

The correct option is B a straight lineLet z =x +iy where x,y ϵ R We have,|iz 1|+|z i|=2 ⇒ |ix y 1|+|x iy i|=2 ⇒√(( y 1)^2 +x^2)+√(x^2+(y 1)^2)=2 ⇒ x^2=0 or x ...

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Byju's Answer

Standard XI

Mathematics

General Form of a Straight Line

Locus of the ...

Question

Locus of the point z satisfying the equation |i z -1|+|z -i|=2 is

a straight line

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a circle

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an ellipse

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a pair of straight lines

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Solution

The correct option is A a straight line
Let z =x +iy where x,y $ϵ R$
$W e h a v e, | i z - 1 | + | z - i | = 2 \Rightarrow | i x - y - 1 | + | x - i y - i | = 2 \Rightarrow \sqrt{(- y - 1)^{2} + x^{2}} + \sqrt{x^{2} + (y - 1)^{2}} = 2 \Rightarrow x^{2} = 0 o r x = 0$
$∴$ The locus of z is a straight line.

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Locus of the point z satisfying the equation |i z -1|+|z -i|=2 is

The correct option is A a straight lineLet z =x +iy where x,y ϵR We have,|iz−1|+|z−i|=2⇒|ix−y−1|+|x−iy−i|=2⇒√(−y−1)2+x2+√x2+(y−1)2=2⇒x2=0orx=0 ∴ The locus of z is a straight line.