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The angle of rotation of axes so that $2 x + 3 y - 7 = 0$ transformed as x=k is

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$\tan^{- 1} \frac{3}{2}$

$\frac{π}{6}$

$\tan^{- 1} (\frac{- 2}{3})$

$\frac{π}{4}$

answer is A.

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Detailed Solution

$2 x + 3 y - 7 = 0$

Transformed equation is $2 (xcosα - ysinα) + 3$ $(xsinα + ycosα) - 7 = 0$
Coeff of y=0 $\Rightarrow - 2 sinα + 3 cosα = 0$ $∴ tanα = \frac{3}{2} \Rightarrow$ $α = \tan^{- 1} \frac{3}{2}$

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