JEE MAIN - Mathematics (2022 - 25th July Evening Shift - No. 1)
For $$z \in \mathbb{C}$$ if the minimum value of $$(|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)$$ is $$5 \sqrt{2}$$, then a value Question: of $$p$$ is _____________.
3
$$\frac{7}{2}$$
4
$$\frac{9}{2}$$
Explanation
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It is sum of distance of z from $$\left( {3\sqrt 2 ,0} \right)$$ and $$\left( {0,p\sqrt 2 } \right)$$
For minimising, z should lie on AB and $$AB = 5\sqrt 2 $$
$${(AB)^2} = 18 + 2{p^2}$$
$$p = \, \pm \,4$$
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