If z - x - i y and - z - ai - z - ai - then the locus of z isA- real axisB- imaginary axisC- x-y D- x2-y2-1

Let z=x+iy |z ai|=|z+ai| ⇒ |x+i(y a)|=|x+i(y+a)| ⇒√(x^2+(y a)^2)=√(x^2+(y+a)^2) Squaring both the sides, we get, x^2+(y a)^2=x^2+(y+a)^2 ⇒ y=0 Which is equatio ...

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Standard XII

Mathematics

Modulus of a Complex Number

If z = x + i ...

Question

If $z = x + i y$ and $| z - a i | = | z + a i |$ then the locus of $z$ is

real axis

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imaginary axis

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x = y

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x^{2} + y^{2} = 1

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Solution

The correct option is A real axis
Let $z = x + i y$
$| z - a i | = | z + a i |$
$\Rightarrow | x + i (y - a) | = | x + i (y + a) |$
$\sqrt{x^{2} + (y - a)^{2}} = \sqrt{x^{2} + (y + a)^{2}}$
Squaring both the sides, we get,
$x^{2} + (y - a)^{2} = x^{2} + (y + a)^{2}$
$\Rightarrow y = 0$ , which is equation of real axis

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Modulus of a Complex Number

Standard XII Mathematics

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If z=x+iy and |z−ai|=|z+ai| then the locus of z is

The correct option is A real axisLet z=x+iy |z−ai|=|z+ai| ⇒|x+i(y−a)|=|x+i(y+a)| √x2+(y−a)2=√x2+(y+a)2 Squaring both the sides, we get, x2+(y−a)2=x2+(y+a)2 ⇒y=0, which is equation of real axis

If $z = x + i y$ and $| z - a i | = | z + a i |$ then the locus of $z$ is