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The largest value of r for which the region represented by the set $\left \{ w\epsilon C/\left | w-4-i \right |\leq r \right \}$

is contained in the region represented by the set $\left \{ z\epsilon C/\left | z-1 \right |\leq\left | z+i \right | \right \}$ is equal to:

Option 1)
$\sqrt{17}$

Option 2)
$2\sqrt{2}$

Option 3)
$\frac{3}{2}\sqrt{2}$

Option 4)
$\frac{5}{2}\sqrt{2}$

Answers (2)

best_answer

As we have learned

Perpendicular bisector -

Locus of point equidistant from two given points.

$\left |z-z_{1} \right |=\left |z-z_{2} \right |$

z will lie on perpendicular bisector of line joining $z_{1}$ and $z_{2}$ .

- wherein

$z_{1}$ and $z_{2}$ are any two fixed points . z is a moving point in the plain which is equidistant from $z_{1}$ and $z_{2}$ .so z will lie on perpendicular bisector

Equation of circle -

$\left |z-z_{0} \right |=r$

$z_{0}$ = centre of circle

r= radius of circle

z lies on circle.

- wherein

Locus of z will be a circle as z is always at a fixed distance r from a fixed point $z_{0}$

$z=x+iy$ , $z_{0}=x_{0}+iy_{0}$

1)

2)

3)

distance = $\frac{\left | 4+1 \right |}{\sqrt2}= 5/\sqrt2$

Option 1)

$\sqrt{17}$

Option 2)

$2\sqrt{2}$

Option 3)

$\frac{3}{2}\sqrt{2}$

Option 4)

$\frac{5}{2}\sqrt{2}$

Posted by

Himanshu

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