For z∈ℂ if the minimum value of (|z−32|+|z−p2i|) is 52, then a value of p is _____________

It is sum of distance of z from (32,0) and (0,p2) For minimising, z should lie on AB and AB=52(AB)2=18+2p2⇒18+2p2=50 ⇒p=±4

For z∈ℂ if the minimum value of (|z−32|+|z−p2i|) is 52, then a value of p is _____________

It is sum of distance of z from (32,0) and (0,p2) For minimising, z should lie on AB and AB=52(AB)2=18+2p2⇒18+2p2=50 ⇒p=±4

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For $z \in ℂ$ if the minimum value of $(| z - 3 \sqrt{2} | + | z - p \sqrt{2} i |) is 5 \sqrt{2}$ , then a value of p is _____________

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$\frac{9}{2}$

$\frac{7}{2}$

answer is C.

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Detailed Solution

Question Image
$It is sum of distance of z from (3 \sqrt{2}, 0) and (0, p \sqrt{2})$
$For minimising, z should lie on A B and A B = 5 \sqrt{2}$
$\begin{array}{l} (A B)^{2} = 18 + 2 p^{2} \Rightarrow 18 + 2 p^{2} = 50 \\ \Rightarrow p = \pm 4 \end{array}$