The transformed equation of x^2+y^2=r^2 when | vedclass

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(A) The given equation is $x^2+y^2=r^2$. When the axes are rotated through an angle $	heta = 36^{\circ}$,the transformation equations are: $x = X \co

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$X^2+Y^2=r^2$

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(A) The given equation is $x^2+y^2=r^2$. When the axes are rotated through an angle $	heta = 36^{\circ}$,the transformation equations are: $x = X \cos 36^{\circ} - Y \sin 36^{\circ}$ $y = X \sin 36^{\circ} + Y \cos 36^{\circ}$ Substituting these into the original equation: $(X \cos 36^{\circ} - Y \sin 36^{\circ})^2 + (X \sin 36^{\circ} + Y \cos 36^{\circ})^2 = r^2$ Expanding the terms: $X^2 \cos^2 36^{\circ} + Y^2 \sin^2 36^{\circ} - 2XY \sin 36^{\circ} \cos 36^{\circ} + X^2 \sin^2 36^{\circ} + Y^2 \cos^2 36^{\circ} + 2XY \sin 36^{\circ} \cos 36^{\circ} = r^2$ Simplifying: $X^2(\cos^2 36^{\circ} + \sin^2 36^{\circ}) + Y^2(\sin^2 36^{\circ} + \cos^2 36^{\circ}) = r^2$ Since $\cos^2 	heta + \sin^2 	heta = 1$,we get: $X^2(1) + Y^2(1) = r^2$ $X^2 + Y^2 = r^2$

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is

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