(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 $

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 4-1.Complex numbers Geometry of complex numbers

Difficult

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

AP EAMCET 2017 All AP EAMCET

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

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-1.Complex numbers

Subtopic

Geometry of complex numbers

Previous Year

AP EAMCET 2017 Paper All AP EAMCET years →

The area of the triangle whose vertices are $i, \omega$ and $\omega^2$ is (Where $\omega$ is a complex cube root of unity other than $1$,$i$ is an imaginary number) . . . . . . sq.units

MediumMHT CET 2025

View Solution

The locus of the point $z$ satisfying $arg\left( \frac{z - 1}{z + 1} \right) = k$ (where $k$ is non-zero) is

Difficult

View Solution

If ${z_1}, {z_2}, {z_3}$ are affixes of the vertices $A, B$ and $C$ respectively of a triangle $ABC$ having centroid at $G$ such that $z = 0$ is the midpoint of $AG$,then:

Easy

View Solution

If $\cos \alpha + 2 \cos \beta + 3 \cos \gamma = 0$,$\sin \alpha + 2 \sin \beta + 3 \sin \gamma = 0$ and $\alpha + \beta + \gamma = \pi$,then $\sin 3 \alpha + 8 \sin 3 \beta + 27 \sin 3 \gamma$ is equal to

MediumKCET 2012

View Solution

If $z$ is a complex number such that $|z| \geq 1$,then the minimum value of $\left|z+\frac{1}{2}(3+4 i)\right|$ is:

MediumJEE MAIN 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

The area of the triangle whose vertices are $i, \omega$ and $\omega^2$ is (Where $\omega$ is a complex cube root of unity other than $1$,$i$ is an imaginary number) . . . . . . sq.units

The locus of the point $z$ satisfying $arg\left( \frac{z - 1}{z + 1} \right) = k$ (where $k$ is non-zero) is

If ${z_1}, {z_2}, {z_3}$ are affixes of the vertices $A, B$ and $C$ respectively of a triangle $ABC$ having centroid at $G$ such that $z = 0$ is the midpoint of $AG$,then:

If $\cos \alpha + 2 \cos \beta + 3 \cos \gamma = 0$,$\sin \alpha + 2 \sin \beta + 3 \sin \gamma = 0$ and $\alpha + \beta + \gamma = \pi$,then $\sin 3 \alpha + 8 \sin 3 \beta + 27 \sin 3 \gamma$ is equal to

If $z$ is a complex number such that $|z| \geq 1$,then the minimum value of $\left|z+\frac{1}{2}(3+4 i)\right|$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module