MHB The tangent and the normal to the conic

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The discussion focuses on the properties of the tangent and normal lines to the conic defined by the equation x²/a² + y²/b² = 1 at a specific point. It highlights that these lines intersect the major axis at points P and P', with the distance PP' equal to a. The equation e²cos²θ + cosθ - 1 = 0 is derived, where e represents the eccentricity of the conic. Participants are encouraged to share their progress or initial thoughts to facilitate more effective assistance. The emphasis is on collaborative problem-solving in understanding conic sections.
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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
 
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Hello debrajr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
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