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Two perpendicular tangents $\mathrm { P A }$ and $\mathrm { P B }$ are drawn to curve $\mathrm { y^2=k x }$ , where $\mathrm { k }$ is maximum value of $\mathrm { (2 \sqrt{3} \sin \theta+2 \cos \theta) }$ and if $\mathrm { p }$ is the length of $\mathrm { AB }$ satisfying in equation $\mathrm { \log _2 \log _3 \log _4 p<0 }$ , then the range of $\mathrm { p }$ is

Option: 1
$(0,32)$

Option: 2
$(0,64)$

Option: 3
$(4,64)$

Option: 4
$(4,64)$

Answers (1)

best_answer

$\mathrm { k=\sqrt{(2 \sqrt{3})^2+(2)^2}=4}$
As $\mathrm { AB}$ is the focal chord of the parabola $\mathrm {y^2=4 x \: \: so\: \: p \geq 4.}$

$\mathrm {\therefore Also \log _2 \log _3 \log _4 p<0 \Rightarrow p<64}$

$\mathrm {\Rightarrow p \in[4,64]}$

Posted by

Sanket Gandhi

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