The locus of the point of intersection of tan | vedclass

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(B) The equation of the tangent to the circle $x^2 + y^2 = a^2$ at the point with parametric angle $\alpha$ is $x \cos \alpha + y \sin \alpha = a$. Le

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Circle

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(B) The equation of the tangent to the circle $x^2 + y^2 = a^2$ at the point with parametric angle $\alpha$ is $x \cos \alpha + y \sin \alpha = a$. Let the two points have parametric angles $	heta$ and $	heta + \pi / 2$. The equations of the tangents at these points are: $L_1: x \cos 	heta + y \sin 	heta = a$ $L_2: x \cos(	heta + \pi / 2) + y \sin(	heta + \pi / 2) = a$,which simplifies to $-x \sin 	heta + y \cos 	heta = a$. To find the locus,square and add the two equations: $(x \cos 	heta + y \sin 	heta)^2 + (-x \sin 	heta + y \cos 	heta)^2 = a^2 + a^2$ $x^2(\cos^2 	heta + \sin^2 	heta) + y^2(\sin^2 	heta + \cos^2 	heta) = 2a^2$ $x^2 + y^2 = 2a^2$. This is the equation of a circle with radius $a \sqrt{2}$.

The locus of the point of intersection of tangents to the circle $x = a \cos \theta, y = a \sin \theta$ at the points whose parametric angles differ by $\pi / 2$ is:

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