Let z 1-16-6 i - z 2-10-6 i where i -1 - If z is any complex number such that amp z - z 1- z - z 2 is -4- then which of the following is-are always correct-A- Locus of z is minor arc of a circleB- Locus of z is major arc of a circleC- - z -13-9 i -3 -2D- - z -13-3 i -3 -2

The correct options are B Locus of z is major arc of a circle C |z 13 9i| = 3 √(2) Locus is major arc of circle ∴ |z 13 9i| = √((13 10)^2 + (9 6)^2) ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Equation of Circle in Complex Form

Let z 1=16+6 ...

Question

Let $z_{1} = 16 + 6 i, z_{2} = 10 + 6 i$ (where $i = \sqrt{- 1})$ . If z is any complex number such that amp $(\frac{z - z_{1}}{z - z_{2}})$ is $\frac{π}{4}$ , then which of the following is/are always correct?

Locus of z is minor arc of a circle

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Locus of z is major arc of a circle

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$| z - 13 - 9 i | = 3 \sqrt{2}$

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$| z - 13 - 3 i | = 3 \sqrt{2}$

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Solution

The correct options are
B
Locus of z is major arc of a circle

C
$| z - 13 - 9 i | = 3 \sqrt{2}$

Locus is major arc of circle

$∴ | z - 13 - 9 i | = \sqrt{(13 - 10)^{2} + (9 - 6)^{2}}$

$\Rightarrow | z - 13 - 9 i | = 3 \sqrt{2}$

Suggest Corrections

Similar questions

Q. Let

z_{1} = 10 + 6 i

and

z_{2} = 4 + 6 i,

where

i = \sqrt{- 1} .

z

is any complex number such that

arg (\frac{z - z_{1}}{z - z_{2}}) = \frac{π}{4},

then the value of

| z - 7 - 9 i |

Q. Let

z_{1} = 10 + 6 i

and

z_{2} = 4 + 6 i

If z is any complex number such that the argument of

(\frac{z - z_{1}}{z - z_{2}})

\frac{π}{4}

then prove that

| z - 7 - 9 i | = 3 \sqrt{2}

Q. Let

z_{1} = 10 + 6 i

and

z_{2} = 4 + 6 i,

where

i = \sqrt{- 1} .

z

is any complex number such that

arg (\frac{z - z_{1}}{z - z_{2}}) = \frac{π}{4},

then the value of

| z - 7 - 9 i |

Q. Let

z_{1} = 10 + 6 i

and

z_{2} = 4 + 6 i

. If

z

is any complex number such that the argument of

(z - z_{1}) / (z - z_{2})

π / 4

, then

| z - 7 - 9 i |

Let $z_{1} = 10 + 6 i$ and $z_{2} = 4 + 6 i$ . If $z$ is a complex number such that the argument of $(z - z_{1}) / (z - z_{2})$ is $π / 4$ , then prove that $| z - 7 - 9 i | = 3 \sqrt{2}$ .

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Let z1=16+6i,z2=10+6i (where i=√−1). If z is any complex number such that amp (z−z1z−z2) is π4, then which of the following is/are always correct?

The correct options are B Locus of z is major arc of a circle C |z−13−9i|=3√2 Locus is major arc of circle ∴|z−13−9i|=√(13−10)2+(9−6)2 ⇒|z−13−9i|=3√2

Let $z_{1} = 16 + 6 i, z_{2} = 10 + 6 i$ (where $i = \sqrt{- 1})$ . If z is any complex number such that amp $(\frac{z - z_{1}}{z - z_{2}})$ is $\frac{π}{4}$ , then which of the following is/are always correct?

The correct options are
B
Locus of z is major arc of a circle

C
$| z - 13 - 9 i | = 3 \sqrt{2}$

Locus is major arc of circle

$∴ | z - 13 - 9 i | = \sqrt{(13 - 10)^{2} + (9 - 6)^{2}}$

$\Rightarrow | z - 13 - 9 i | = 3 \sqrt{2}$