The gradient of the tangent line at the point | vedclass

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Question

(D) The equation of the tangent at point $(a \cos \alpha, a \sin \alpha)$ to the circle $x^2 + y^2 = a^2$ is given by $x(a \cos \alpha) + y(a \sin \al

Vedclass · Accepted Answer

$ - \cot \alpha $

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(D) The equation of the tangent at point $(a \cos \alpha, a \sin \alpha)$ to the circle $x^2 + y^2 = a^2$ is given by $x(a \cos \alpha) + y(a \sin \alpha) = a^2$.Rearranging this into the slope-intercept form $y = mx + c$,we get $y = -\frac{\cos \alpha}{\sin \alpha} x + \frac{a}{\sin \alpha}$.Thus,the gradient (slope) $m$ is $- \frac{\cos \alpha}{\sin \alpha} = - \cot \alpha$.

The gradient of the tangent line at the point $(a \cos \alpha, a \sin \alpha)$ to the circle $x^2 + y^2 = a^2$ is

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