The locus of the intersection point of x cos | vedclass

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(D) Given equations are:$x \cos \alpha - y \sin \alpha = a$  $(1)$$x \sin \alpha - y \cos \alpha = b$  $(2)$Squaring and adding $(1)$ and $(2)$:$(x \c

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None of these

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(D) Given equations are:$x \cos \alpha - y \sin \alpha = a$  $(1)$$x \sin \alpha - y \cos \alpha = b$  $(2)$Squaring and adding $(1)$ and $(2)$:$(x \cos \alpha - y \sin \alpha)^2 + (x \sin \alpha - y \cos \alpha)^2 = a^2 + b^2$$x^2(\cos^2 \alpha + \sin^2 \alpha) + y^2(\sin^2 \alpha + \cos^2 \alpha) - 2xy \sin \alpha \cos \alpha - 2xy \sin \alpha \cos \alpha = a^2 + b^2$$x^2 + y^2 - 2xy \sin(2 \alpha) = a^2 + b^2$This equation represents a conic section whose nature depends on the value of $\alpha$. Since the locus is not a standard ellipse,hyperbola,or parabola for all $\alpha$,the correct option is $D$.

The locus of the intersection point of $x \cos \alpha - y \sin \alpha = a$ and $x \sin \alpha - y \cos \alpha = b$ is

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