(C) The given equation is of the form $|z-z_1| + |z-z_2| = 2a$,where $z_1 = 3i$ and $z_2 = -3i$.This represents an ellipse with foci at $(0, 3)$ and $

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Ellipse with eccentricity $\frac{3}{5}$

(C) The given equation is of the form $|z-z_1| + |z-z_2| = 2a$,where $z_1 = 3i$ and $z_2 = -3i$.This represents an ellipse with foci at $(0, 3)$ and $(0, -3)$.The distance between the foci is $2ae = |z_1 - z_2| = |3i - (-3i)| = |6i| = 6$.Given $2a = 10$,so $a = 5$.Using the relation $2ae = 6$,we get $5e = 3$,which implies $e = \frac{3}{5}$.Thus,the locus is an ellipse with eccentricity $\frac{3}{5}$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Geometry of complex numbers

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If $z=x+iy$ and if the point $P$ in the Argand plane represents $z$,then the locus of $P$ satisfying the equation $|z-3i|+|z+3i|=10$ is

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A
Circle with centre $(-3,3)$
B
Hyperbola with eccentricity $\frac{5}{3}$
C
Ellipse with eccentricity $\frac{3}{5}$
D
Ellipse with eccentricity $\frac{4}{5}$

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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If $z=x+iy$ and if the point $P$ in the Argand plane represents $z$,then the locus of $P$ satisfying the equation $|z-3i|+|z+3i|=10$ is

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