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(A) The given equation is $y^2 + kxy - x^2 	an^2 A = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = -	an^2 A$,$2h =

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(A) The given equation is $y^2 + kxy - x^2 	an^2 A = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = -	an^2 A$,$2h = k$,and $b = 1$.The angle $	heta$ between the lines is given by $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$.Here $	heta = 2A$,so $	an 2A = \frac{2\sqrt{(k/2)^2 - (-	an^2 A)(1)}}{1 - 	an^2 A} = \frac{2\sqrt{\frac{k^2}{4} + 	an^2 A}}{1 - 	an^2 A}$.We know that $	an 2A = \frac{2 	an A}{1 - 	an^2 A}$.Equating the two expressions: $\frac{2 	an A}{1 - 	an^2 A} = \frac{2\sqrt{\frac{k^2}{4} + 	an^2 A}}{1 - 	an^2 A}$.This implies $	an A = \sqrt{\frac{k^2}{4} + 	an^2 A}$.Squaring both sides: $	an^2 A = \frac{k^2}{4} + 	an^2 A$.Therefore,$\frac{k^2}{4} = 0$,which gives $k = 0$.

If the angle between the lines represented by the equation $y^2 + kxy - x^2 \tan^2 A = 0$ is $2A$,then $k = $

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