The locus of a point z in the Argand plane th | vedclass

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

Question

(D) Let $F_1$ be the point $(1, -1)$ and $F_2$ be the point $(2, 1)$.The given equation is $|z - F_1| - |z - F_2| = 3$,which represents the difference

Vedclass · Accepted Answer

none of the above

Vedclass · Answer

(D) Let $F_1$ be the point $(1, -1)$ and $F_2$ be the point $(2, 1)$.The given equation is $|z - F_1| - |z - F_2| = 3$,which represents the difference of distances from two fixed points.The distance between the foci $F_1$ and $F_2$ is $d = |F_1F_2| = \sqrt{(2 - 1)^2 + (1 - (-1))^2} = \sqrt{1^2 + 2^2} = \sqrt{5}$.For a hyperbola defined by $|PF_1 - PF_2| = 2a$,the condition $2a Here,$2a = 3$ and $d = \sqrt{5} \approx 2.236$.Since $3 > \sqrt{5}$,the condition $2a Therefore,no such point $z$ exists in the Argand plane that satisfies the given equation.

The locus of a point $z$ in the Argand plane that moves satisfying the equation $|z - (1 - i)| - |z - (2 + i)| = 3$ is:

Similar Questions

The area of the triangle whose vertices are represented by the complex numbers $0, z,$ and $z{e^{i\alpha }}$ $(0 < \alpha < \pi )$ is equal to:

If the four complex numbers $z$,$\overline{z}$,$\overline{z}-2 \operatorname{Re}(\overline{z})$ and $z-2 \operatorname{Re}(z)$ represent the vertices of a square of side $4$ units in the Argand plane,then $|z|$ is equal to:

For all $z \in \mathbb{C}$ on the curve $C_1: |z| = 4$,let the locus of the point $w = z + \frac{1}{z}$ be the curve $C_2$. Then:

Let $S_{1}, S_{2}$ and $S_{3}$ be three sets defined as:
$S_{1} = \{ z \in C : |z - 1| \leq \sqrt{2} \}$
$S_{2} = \{ z \in C : \operatorname{Re}((1 - i)z) \geq 1 \}$
$S_{3} = \{ z \in C : \operatorname{Im}(z) \leq 1 \}$
Then the set $S_{1} \cap S_{2} \cap S_{3}$

The area (in sq units) of the triangle whose vertices are the points represented by the complex numbers $0, z$,and $z e^{i \alpha}$ $(0 < \alpha < \pi)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module