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In the given figure $Δ A B C$ is right angled at B. If AB = 4 and BC = 3 and side AC slides along the coordinate axes in such a way that ‘B’ always remains in the first quadrant, then locus of B is

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3y = 4x

$3 x^{2} = 4 y^{2}$

$x^{2} = y^{2}$

3y + 4x = 0

answer is B.

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Detailed Solution

$\tan θ = \frac{3}{4}$ (from Fig.)
$\Rightarrow$ Slope of $O B = \tan (\frac{π}{2} - θ) = \cot θ$
Question Image
$\Rightarrow$ Locus of (h, k) is $\frac{k}{h} = \frac{4}{3} \Rightarrow 3 y - 4 x = 0$

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