Current Score : 30 / 32 Due : Friday, May 10, 2019 11:59 PM EDT1. 5/6 points | Previous AnswersSCalcET8 10.3.003.Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.(a) (b) 10.3 (Homework)samantha OhMath 142 LR-X, section LR-X, Spring 2019Instructor: Kathlene HockadayWebAssignLast Saved : n/a Saving... ()(5, 3π/2)(x, y) = 0,−5 (5 , π/4)2(c) (x, y) = 5,5 (−5, −π/6)(x, y) = −4√32,322. 4/4 points | Previous AnswersSCalcET8 10.3.005.The Cartesian coordinates of a point are given.(a) (i) Find polar coordinates of the point, where and (ii) Find polar coordinates of the point, where and (b) (i) Find polar coordinates of the point, where and (ii) Find polar coordinates of the point, where and (−3, 3)(r, θ) r > 0 0 ≤ θ < 2π.(r, θ) = 3√2, 3π4 (r, θ) r < 0 0 ≤ θ < 2π.(r, θ) = −3√2, 7π4 (2, 2 )3(r, θ) r > 0 0 ≤ θ < 2π.(r, θ) = 4, π3 (r, θ) r < 0 0 ≤ θ < 2π.(r, θ) = −4, 4π33. 1/1 points | Previous AnswersSCalcET8 10.3.008.Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. 0 ≤ r < 2, π ≤ θ ≤ 3π/24. 2/2 points | Previous AnswersSCalcET8 10.3.015.Find a Cartesian equation for the curve and identify it.x2+y2=5 5. 2/2 points | Previous AnswersSCalcET8 10.3.017.Find a Cartesian equation for the curve and identify it.(x−72)2+y2=494 r2 = 5limaçonellipse hyperbolacircleparabolar = 7 cos(θ)ellipsehyperbola parabolalimaçoncircle6. 2/2 points | Previous AnswersSCalcET8 10.3.019.Find a Cartesian equation for the curve and identify it.x2−y2=1 7. 1/1 points | Previous AnswersSCalcET8 10.3.021.Find a polar equation for the curve represented by the given Cartesian equation.r=6sin(θ) 8. 1/1 points | Previous AnswersSCalcET8 10.3.025.Find a polar equation for the curve represented by the given Cartesian equation.r=8ccos(θ) r2 cos(2θ) = 1circleellipse limaçonparabolahyperbolay = 6x2 + y2 = 8cx9. 2/2 points | Previous AnswersSCalcET8 10.3.027.For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then writean equation for the curve.(a) A line through the origin that makes an angle of π/3 with the positive x-axis.θ=π3 (b) A vertical line through the point (1, 1).x=1 10.1/1 points | Previous AnswersSCalcET8 10.3.030.Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.r = 1 − cos(θ)11.1/1 points | Previous AnswersSCalcET8 10.3.032.Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates. r = 1 + 5 cos(θ)12.1/1 points | Previous AnswersSCalcET8 10.3.041.Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates. r2 = 4 sin(2θ)13.0/1 points | Previous AnswersSCalcET8 10.3.057.Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.0 14.1/1 points | Previous AnswersSCalcET8 10.3.058.Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.−√3 15.6/6 points | Previous AnswersSCalcET8 10.3.503.XP.Find the Cartesian coordinates of the given polar coordinates. Then plot the point.(a) r = 6/θ, θ = πr = cos(θ/3), θ = π(2, π)(x, y) = −2,0(b) (6, −2π/3)(x, y) = −3,−3√3(c) (−6, 3π/4)(x, y) =