For all values of theta,the locus of the poin | vedclass

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(B) Given the lines:$1) x \cos 	heta + y \sin 	heta = a$$2) x \sin 	heta - y \cos 	heta = b$Squaring and adding both equations:$(x \cos 	heta + y

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$A$ circle

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(B) Given the lines:$1) x \cos 	heta + y \sin 	heta = a$$2) x \sin 	heta - y \cos 	heta = b$Squaring and adding both equations:$(x \cos 	heta + y \sin 	heta)^2 + (x \sin 	heta - y \cos 	heta)^2 = a^2 + b^2$$x^2 \cos^2 	heta + y^2 \sin^2 	heta + 2xy \sin 	heta \cos 	heta + x^2 \sin^2 	heta + y^2 \cos^2 	heta - 2xy \sin 	heta \cos 	heta = a^2 + b^2$$x^2(\cos^2 	heta + \sin^2 	heta) + y^2(\sin^2 	heta + \cos^2 	heta) = a^2 + b^2$$x^2 + y^2 = a^2 + b^2$This represents the equation of a circle with center $(0, 0)$ and radius $\sqrt{a^2 + b^2}$.

For all values of $\theta$,the locus of the point of intersection of the lines $x \cos \theta + y \sin \theta = a$ and $x \sin \theta - y \cos \theta = b$ is

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