Let the locus of any point P(z) in the argand plane is arg((z - 5 i/z + 5 i))=(π /4). If O is the origin, then the value of (m a x . (O P) + m i n . (O P)/2) is

Question

Let the locus of any point P(z) in the argand plane is arg((z - 5 i/z + 5 i))=(π /4). If O is the origin, then the value of (m a x . (O P) + m i n . (O P)/2) is (A) 5√2 (B) 5+(5/√2) (C) 5+5√2 (D) 10-(5/√2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-2kv1ispuqrhekrx0.jpg" /> Since, r2+r2=102 ⇒ r=5√2 max.(O P)=OC+ radius =5+5√2 and min.(O P)=OA=5 Required value =(5 + 5 + 5 √2/2)=5+(5/√2) .

Q. Let the locus of any point $P (z)$ in the argand plane is $a r g (\frac{z - 5 i}{z + 5 i}) = \frac{π}{4} .$ If $O$ is the origin, then the value of $\frac{ma x . ( OP ) + min . ( OP )}{2}$ is

$52$

$5 + \frac{5}{2}$

$5 + 52$

$10 - \frac{5}{2}$

Since, $r^{2} + r^{2} = 1 0^{2}$
$\Rightarrow r = 52$
$ma x . (OP) = OC +$ radius
$= 5 + 52$
and $min . (OP) = O A = 5$
Required value $= \frac{5 + 5 + 5 2}{2} = 5 + \frac{5}{2}$ .

Q. Let the locus of any point P(z) in the argand plane is arg(z+5iz−5i​)=4π​. If O is the origin, then the value of 2max.(OP)+min.(OP)​ is

52​

5+2​5​

5+52​

10−2​5​