Let C be the rose defined in polar coordinates as r = 2 cos(20), 0 = [0, 2π]. (a) Find all points (x(0), y(0)) in C, for which the slope of the tangent line to Cat (x(0), y(0)) is equal to tan(0). (b) Deduce from part (a) that there is no circle S with positive radius centered at the origin, for which C and S would intersect perpendicularly at some point. [Hint: For part (b), notice that if L is the straight line passing through the origin and a point (x(0), y(0)) lying on a circle S centered at the origin, then L is perpendicular to S at (x(0), y(0)), and it has the equation y tan(0).x.]

Let C be the rose defined in polar coordinates as r = 2 cos(20), 0 = [0, 2π]. (a) Find all points (x(0), y(0)) in C, for which the slope of the tangent line to Cat (x(0), y(0)) is equal to tan(0). (b) Deduce from part (a) that there is no circle S with positive radius centered at the origin, for which C and S would intersect perpendicularly at some point. [Hint: For part (b), notice that if L is the straight line passing through the origin and a point (x(0), y(0)) lying on a circle S centered at the origin, then L is perpendicular to S at (x(0), y(0)), and it has the equation y tan(0).x.]

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Please provide a hand written solution, with working of all steps shown properly.

Let C be the rose defined in polar coordinates as r = 2 cos(20), 0 = [0, 2π].
(a)
Find all points (x(0), y(0)) in C, for which the slope of the tangent line to C at
(x(0), y(0)) is equal to tan(0).
(b)
Deduce from part (a) that there is no circle S with positive radius centered at the
origin, for which C and S would intersect perpendicularly at some point.
[Hint: For part (b), notice that if L is the straight line passing through the origin and a point (x(0), y(0))
lying on a circle S centered at the origin, then L is perpendicular to S at (x(0), y(0)), and it has the
equation y = tan(0).x.]

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