debrajr
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The tangent and the normal to the conic
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
at a point $$(a\cos\left({\theta}\right), b\sin\left({\theta}\right))$$
meet the major axis in the points $$P$$ and $$P'$$, where $$PP'=a$$
Show that $$e^2cos^2\theta + cos\theta -1 = 0$$, where $$e$$ is the eccentricity of the conic
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
at a point $$(a\cos\left({\theta}\right), b\sin\left({\theta}\right))$$
meet the major axis in the points $$P$$ and $$P'$$, where $$PP'=a$$
Show that $$e^2cos^2\theta + cos\theta -1 = 0$$, where $$e$$ is the eccentricity of the conic