If - z - 2 - 3i - - - z - 2 - 6i - - 4- where i - -1- then locus of P z is

The correct option is A an ellipse | z ( 2+3i ) #160; | +| z+( 2 6i ) #160; | =4 Shows that sum of distances of z from two fixed points (2+3i) an ...

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Standard XII

Mathematics

Modulus of a Complex Number

If | z - 2 ...

Question

If $| z - 2 - 3 i | + | z + 2 - 6 i | = 4$ , where $i = \sqrt{- 1}$ , then locus of $P (z)$ is

an ellipse

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ϕ

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line segment of points

2 + 3 i

and

- 2 + 6 i

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None of these

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Solution

The correct option is A an ellipse
$| z - (2 + 3 i) | + | z + (2 - 6 i) | = 4$
Shows that sum of distances of z from two fixed points $(2 + 3 i)$ and $- (2 - 6 i)$ is constant and this is the property of ellipse.
Therefore locus of z is ellipse.

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If |z−2−3i|+|z+2−6i|=4, where i=√−1, then locus of P(z) is

The correct option is A an ellipse|z−(2+3i)|+|z+(2−6i)|=4Shows that sum of distances of z from two fixed points (2+3i) and −(2−6i) is constant and this is the property of ellipse.Therefore locus of z is ellipse.

If $| z - 2 - 3 i | + | z + 2 - 6 i | = 4$ , where $i = \sqrt{- 1}$ , then locus of $P (z)$ is

The correct option is A an ellipse
$| z - (2 + 3 i) | + | z + (2 - 6 i) | = 4$
Shows that sum of distances of z from two fixed points $(2 + 3 i)$ and $- (2 - 6 i)$ is constant and this is the property of ellipse.
Therefore locus of z is ellipse.