Part A and B neededBy Hand solution neededPlease provide me hundred percent correct solution in the order to get positive feedback please show me neat and clean work for it by hand solution needed (a)0, then(d)(e)४P(x₁, y₁)F₁ (-₁0)-Ltan 0) Prove the following useful result: If two lines L₁ and L₂ intersect at an anglem₂ - m₁1+mim2where my and m₂ are the slopes of L₁ and L₂ respectively.tan x-tanyHint: tan(x - y) = 1+tan x tan yĘ₂(c/o)(b) ((c) (3) Show that tana = Hint: recall that c² = a²-6². Warning! The algebrawill get messy! Your job is to clean up the mess!cylDetermine the slope of L in terms of a, b, a, and y₁.6²) Use (c) to show that a = 3.You have just proved the reflection property of ellipses! This property explainshow whispering galleries, elliptical billiards and lithotripsy work. Write an amusingessay (maximum 150 words) on an interesting application of the reflection property ofellipses. You can include illustrations in your essay. Let P (1,91) be a point on the ellipsey²6²1.Let F₁ and F₂ be the foci of the ellipse. Let L be the tangent line to the ellipse at P = (x₁, Y₁).Let a and 3 be the angles between the lines PF1, PF2 and L as shown in the figure.

Concept Used The slope of a line is the change in the y coordinate with respect to the change in the…

(a) 0, then Р(хо, у,) (b) ( F₁ (-₁0) ) Prove the following useful result: If two lines L₁ and L2 intersect at an angle tan 8 = m₂ - m₁ 1+m₁m₂ where m, and m₂ are the slopes of L₁ and L₂ respectively. tan x-tany Hint: tan(x - y) 1+tan x tan y Determine the slope of L in terms of a, b, 1 and y₁. Ę₂ (c/o)

(a) 0, then Р(хо, у,) (b) ( F₁ (-₁0) ) Prove the following useful result: If two lines L₁ and L2 intersect at an angle tan 8 = m₂ - m₁ 1+m₁m₂ where m, and m₂ are the slopes of L₁ and L₂ respectively. tan x-tany Hint: tan(x - y) 1+tan x tan y Determine the slope of L in terms of a, b, 1 and y₁. Ę₂ (c/o)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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