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Question Number 46084 by peter frank last updated on 20/Oct/18

Commented by peter frank last updated on 21/Oct/18

$$\mathrm{help}$$

Answered by ajfour last updated on 21/Oct/18

$$A\equiv [a\cos (\alpha +\beta ),b\sin (\alpha +\beta )]$$$$B\equiv [a\cos (\alpha -\beta ),b\sin (\alpha -\beta )]$$$$\underset{-}{slopeofchord}$$$$=\frac{b}{a}\left(\frac{\cos \alpha \sin \beta }{-\sin \alpha \sin \beta }\right)=-\frac{b}{a}\cot \alpha$$$$\left(slopeoftangent\right){\mid }_{\theta =\alpha }=\frac{dy}{dx}{\mid }_{\theta =\alpha }$$$$=\left(\frac{dy/d\theta }{dx/d\theta }\right){\mid }_{\theta =\alpha }=-\frac{b\cos \alpha }{a\sin \alpha }.$$

Commented by peter frank last updated on 21/Oct/18

$$\mathrm{thank}\mathrm{you}\mathrm{sir}.$$

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