We prove that the focal radii at a point on an ellipse make equal angles with the tangent line L Let P (x 0 , y 0 ) be a point on the ellipse in Figure 25 with foci F 1 (c, 0) and F 2 (c, 0), and eccentricity e c a Show that the equation of the tangent line at P is Ax By 1, where A x 0 a 2 and B y ...

The equation of the tangent line is y yo m xxo m To find the slope m we implicitly di ...

We prove that the focal radii at a point on an ellipse make equal angles with the

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We prove that the focal radii at a point on an ellipse make equal angles with the tangent line L. Let P = (x₀, y₀) be a point on the ellipse in Figure 25 with foci F₁ = (−c, 0) and F₂ = (c, 0), and eccentricity e = c/a.

L R = (a, B) F = (-c, 0) P = (xo, Yo) 1 01 0 R = (, B) F= (c, 0) x

Show that the equation of the tangent line at P is Ax + By = 1, where A = x₀/a² and B = y₀/b₂.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 25, 2023 08:29 AM

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We prove that the focal radii at a point on an ellipse make equal angles with the

Question:

L R₁ = (α₁, B₁) F₁ = (-c, 0) P = (xo, Yo) 1 01 0₂ R₂ = (α₂, B₂) F₂= (c, 0) →x

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The equation of the tangent line is y yo m xxo m To find the slope m we implicitly di...View the full answer

Calculus

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