only question 3 complete please 1.(a) Find the equation of the plane PL which contains the three pointsA = (1,0,1), B = (-1,2,5), and C= (5,1, -1).(b) Find the parametric equation of a line L which passes through the originand is perpendicular to PL.2. Consider the curve given byr(0)=2+2 cos 0, 0≤0 ≤2π.(a) Give a rough sketch.(b) Calculate the enclosed area.3. For the curve6= 2 + 6 sinr(0) =(a) Find the eccentricity and the directrix.(b) Describe the curve and provide a sketch.4. Consider the curve given byr(t) = (e-t cos(t), e-t sin(t), 1- e-t), t = [0, 2π].(a) Find the arc length L of this curve.(b) Find the points (if any) where the curve is parallel to the z-axis?

3. (a) Consider the given equation of curve, rθ=62+6sinθ=31+3sinθ Compare with the standard…

Answered: 3. For the curve r(0) = 6 2+6 sin 0 (a)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 53E

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3. For the curve r(0) = 6 2+6 sin 0 (a) Find the eccentricity and the directrix. (b) Describe the curve and provide a sketch.