50 A curve with polar equation r 5 sin 0 + 21 cos e represents a line. This line has a Cartesian equation of the form y = mx + b ,where m and b are constants. Give the formula for y in terms of r. For example, if the line had equation y = 2x + 3 then the answer would be 2 · x + 3. y =

Q: The transform curve of polar equation r 4 cos@+4 sin e to rectangular coordinates (x-2)° – y² = 8…

A: Given that: r=4cosθ+4sinθ

Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

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Q: r = sin(30) r = cos(30) a) Sketch both polar curves on the same graph. b) How far should we let 0…

A: The solution for the above question is as shown below.

Q: ht) A curve with polar equation 9 r = 7 sin 0 + 36 cos 0 ents a line. This line has a Cartesian…

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Q: 19 A curve with polar equation r = 8 sin 0+17 cos 0 represents a line. This line has a Cartesian…

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Q: 2. Graph the given parametric equations using values of t between 0 and 180 degrees. x = 2 cos(3t) ,…

A: Put the values of t in to given equation one by one, find the points

Q: A curve with polar equation r=8/4sinθ+21cosθ represents a line. This line has a Cartesian equation…

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Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

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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: 4. Given the polar equation r =1+sin 0. (a) Sketch the curve by first sketching it in rectangular…

A: Given: The polar equation is r=1+sinθ. To find: a) Sketch the curve by sketching the rectangular…

Q: 39 A curve with polar equation r = 3 sin 0 + 25 cos 0 represents a line. This line has a Cartesian…

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Q: 1. Find a cartesian equation for the curve r² sin 20 = 8.

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Q: 4. Eliminate the parameter to obtain the Cartesian form of the equations x = 5 cos(t), y = 3 sin(t)…

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Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

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Q: r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis

A: rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…

Q: 36 A curve with polar equation r = 29 sin 0 + 7 cos 0 represents a line. Write the equation of the…

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Q: 30 A curve with polar equation = 3 sin 8 + 7 cos e represents à line. This line has a Cartesian…

A: Given, a curve with polar equation…

Q: A curve with polar equation represents a line. This line has a Cartesian equation of the form y = mx…

A: To write the given equation in the form of y  = mx + b.

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: 12 A curve with polar equation r = 4 sin 0 + 33 cos 0 represents a line. This line has a Cartesian…

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Q: 2. a) If -1 o £ 2, give three polar points in the torm of Cr,@) eanivalent to Cartesian point…

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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: 12 Find a Cartesian equation for the polar curver = Solve for y and type the simplified solution in…

A: The given equation is: r=12sin θ-15 cos θ...(1) To convert the polar equation to the cartesian…

Q: The parametric equations x= 4 − 6 sin 4t and y = 6 + 6 cos 4 t for 0 ≤ t ≤ π/3 represent a curve…

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Q: A curve with polar equation r=39/9sin(x)+64cos(x) represents a line. This line has a Cartesian…

A: Equation of the line in polar coordinates  is given byr=399sinθ+64cosθ  ...(1)as we know that…

Q: 10. (a) Given the polar equation r = -4 cos 6. Write the polar equation as a Cartesian equation. (b)…

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Q: 33 A curve with polar equation r 9 sin 0 + 55 cos 0 mx + b,where m and b are represents a line. This…

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Q: A curve with polar equation r = 20 4 sin 0+ 17 cos 0 represents a line. This line has a Cartesian…

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Q: 44 A curve with polar equation r = 7 sin 0 + 36 cos 0 represents a line. This line has a Cartesian…

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Q: The parametric equations of a curve are x cos 20, y = 1 + sin 20. Find dy and dx d²y at 6 1/6. Find…

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Q: 10. Consider the curve with polar equation r = 6 sin 0 where 0< 0 <T. WVithout finding the Cartesian…

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Q: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…

A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…

Q: 23 A curve with polar equation r = 4 sin 0+ 13 cos 0 represents a line. This line has a Cartesian…

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Q: A curve with polar equation 16 6 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

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Q: A curve with polar equation r=42/(9sin(theta)+28cos(theta)) represents a line. This line has a…

A: Given: -

Q: 31 A curve with polar equation r = 3 sin 0 + 7 cos 0 represents a line. This line has a Cartesian…

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Q: The parametric equations x= 5 − 2 sin 3t and y = 3 + 2 cos 3 t for 0 ≤ t ≤ π/4 represent a curve C.…

A: Consider the given parametric equations:

Q: 20 4. An ant walks on a flat surface along a curve with polar equation r= from a point where 0=0 to…

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Q: A curve in polar coordinates is given by: r = 12 + 5 cos 0. Point Pis at 0 = 297 24 (1) Find polar…

A: Given polar curve r=12+5cos(θ)θ=29π24 (a) To find out polar coordinate r for the given P,  Plug in…

Q: A curve with polar equation 29 8 sin 0 + 65 cos 0 represents a line. This line has a Carteslan…

A: Given:- r =29/(8sinθ+65cosθ) To find:- Equation of line in Cartesian form

Q: 7 A curve with polar equationr = 5 sin 0 + 31 cos 0 represents a line. This line has a Cartesian…

A: topic - change in coordinate system

Q: The parametric equations x= 6 − 9 sin 2t and y = 5 + 9 cos 2 t for 0 ≤ t ≤ ?/4 represent a curve C.…

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Q: Find a Cartesian equation for the curve represented by polar equation r= 14 cos 0- 4 sin e. O A. ^…

A: Use the transformation from polar coordinate to Cartesian coordinate and simplify.

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: 23 A curve with polar equation r : 4 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

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Q: 2. (a) A curve has parametric equations x= 3 - 2cos 0and y = sin 8. Determine the Cartesian equation…

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