• Question 1. Given the point R (1,4) outside the circle L = x2 + y2 -2y = 1 <=> x² + y2 - 2y - 1 = 0 Determine the point of tangency of the circle from point R using the help of the polar line. Then draw a circle and the equation of the %3D %3D tangent.

Q: 6. What is the equation of the polar curve shown? a) r = -4 sin 30 c) r = 4 cos 30 b) r = 4 sin 30…

A: Since you have asked multiple question so we will be answering only first question. Given polar…

Q: Question 25 Solve the problem. Write parametric equations for the tangent line to the curve of…

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Q: What type of polar curve does the equation r^2 = 4 cos 2@ represent ?

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Q: The curve whose equation in polar coordinates is given by r -4 sin(@) is a circle with its center…

A: I am going to solve the given problem first by converting in to the cartesian form and then…

Q: Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 2cx

A: Polar equation for the curve represented by the given cartesian equation x2+y2=2cx is r=2c cosθ The…

Q: Find an equation in rectangular coordinates for the curve r^2 = cos 2θ.

A: We know that, the relationship between polar and rectangular co-ordinates are given as r2=x2+y2…

Q: Graph the family of polar equations r = 1 + c sin 2u for c = 0.3, 0.6, 1, 1.5, and 2. How does the…

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Q: Solve the problem. Te 1) Plot the point 2, and find other polar coordinates (r, 0) of the point for…

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Q: Which of the following shows the correct sketch of the polar curve r= 10 sin(3 0)? 10 5 -10 -5 5 10…

A: We solve it by following method.

Q: find a polar equation for the curve represented by the given cartesian equation 5x^2 +y^2 = 8x (r is…

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Q: [Question 5] Write down a complete geometric description of the parametric curve x=2cos0,y=2sine,0s…

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Q: a) A curve has the parametric equation given as x = 4+3 cos 0 y = 3 sin 0 – 2. i) Convert the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Q3 Write down the polar form of the equation 2 arctan(y/a)

A: convert the given equation into polar form x2+y2=e-2arctanyx

Q: With your graphing utility in radian and parametric modes, enter the equations XIT = cos T and Y1T…

A: We have to graph the entered equations and describe the graph and find the the least and greatest…

Q: Which of the following shows the correct sketch of the polar curve r = -9+ 9 sin(0)? 15 5 -15 -10 -5…

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Q: Match the graph with its polar equation. r = 2 sin(0) A/2 л/2 4 2 2 4 A/2 3- A/2 2 -1 2 - 2 -1 1 2

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Q: 3. Consider the curve C of equation 4ry r² + y²" Among the options indicated, select the one that…

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Q: Question 3 Sketch the polar curve with the given equation "= -5 cos 8, OA. 3 4 OB 3 OC. OD. OE. 1 4

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Q: 37. The Cartesian equation of the polar curve 2 = 2a' sin 20 is A. 1? + y? = 4a²xy B. (z* + 3° )° =…

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Q: Problem 4 Parts A, B, and C

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Q: For this problem sketch the curve with the given polar equation for parts a) and b) a) r = - 3…

A: r =-3cos(theta)

Q: Consider the following. x = 6 cos e y = 4 sin e (a) Sketch the curve represented by the parametric…

A: a)Determine the value of x and y for θ=0,π/2

Q: Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular…

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Q: Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in…

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Q: Question 2. Consider the parametric curve C given by the equations x = t – 3, y = t³ – 3t. a) Find…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x² + y2 = 16

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Q: Question 3 Find the value of J sinydx+ (xcosy-sinyldy, where Cis any curve from (2,0) to (1, T). Ca…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r= 2a cos e 4 4

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Q: A curve with polar equation r = 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian…

A: The polar equation is, r=58sinθ+49cosθ   Rewrite the equation. 8rsinθ+49rcosθ=5   Substitute y for…

Q: 9. (a) Find the rectangular coordinates of the point(s) of the graph of the polar equation r = 4 sin…

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Q: QUESTION 4 (a) Express the following Cartesian equation 5x² – 4x – 2+5y? =0 in terms of polar…

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Q: Q1// Converting r= 12 cos 0 r = 12 cos 0 from polar to the equation of a circle?

A: Given problem:- Converting r = 12cos(θ) from polar to the equation of a circle?

Q: 2 Q3: Discuss the symmetry and plot the locus of polar equation r 1-cose

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Q: Question 3 Find the point(s) of intersection of the curves r = 6 and r = 12 sin e OA 6 * (6.5)(6) 3…

A: To find the intersection of the curve r=6 and r=12sinθ

Q: Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 10cx

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Q: 2) Sketch the graph of the curve with the polar equation: r=2- sin(20).

A: The given polar equation is r=2-sin2θ. Draw the graph of the given polar equation in detail.

Q: Question 20 Find the length of the curve. Hint: Use the Arclength formula for parametric equations…

A: Find the length of the given curve

Q: Find the lengths of the curves given by the polar coordinate equations r = 2 sin θ + 2 cos θ, 0 ≤ θ…

A: Given: r=2sinθ+2cosθ; 0≤θ≤π2 for finding length of curve given by the given polar equation, first we…

Q: 4. Find the equation of the circle (in polar) with center on the line a = and passing through the…

A: The general equation of a circle with centre at r∘, θ∘ and radius, a is given by r cos θ-r∘ cos…

Q: 2. Given the equation y =, covert to polar form.

A: For example  Given the equation y = 5 We know that to convert cartesian to polar, We use the…

Q: Consider the curve C of equation 4.xy x² + y? x² + y² From the choices given, select the one that…

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Q: Question 19 Find the center of 2 circles tangent to x² + y = 100 %3D at (6,-8) having a radius of 15…

A: Given: x2 + y2 = 102      center: 0,0, radius = 10                     1Tangent at 6,-8.…

Q: Question 10 Find the rectangular coordinates of the point(s) of intersection of the polar curves r =…

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Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 e R. 4 cos…

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Q: 1- Which of the following is the closest distance from the points on the curve given by the equation…

A: The equation of circle is given by, r = 6 The point in the Cartesian coordinate is (-8, -15) which…

Q: Sketch the graph and the curve represented by x = 3 cos 0 and y = 4 sin 0 ,0 < 0 < 2n by eliminating…

A: The given parametric equation,      x=3cos θ and y=4sin θ, 0≤θ≤2π

Q: (b) Find the graph of the parametric equations: I = sin 0, y = 3 – 2 cos 20

A: Plugging values of θ, to find the corresponding values of x and y: When…

Q: A curve with polar equation 32 3 sin 8 + 13 cos e represents a line. This line has a Cartesian…

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Q: What curve is represented by the polar equation r = 2

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Q: Match the graph with its polar equation. r = 2 sin(0) A/2 A/2 4 2 -2 2 4 - 2 2 - 4 A/2 3| л/2 2 1 1…

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