Find the Cartesian coordinates of the given polar coordinates. Then plot the point. (a) (-V2, 5x/4) (x, y) =

Q: Convert the given functions into the desired coordinates. (a) 2x-5x³=1+xy into polar coordinates,…

A: We have convert the cartesian in to polar and polar in cartesian

Q: Write a polar equation of the form r sin(0 – 0,) = ro for the line 2/3 x+2y = 1. %3D

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Q: Convert the Cartesian Equation to a polar equation.  x2 + y2 = 3y

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Q: convert to an equation in polar coordinates of the form r = f (θ ).  y = x 2

A: Given: y=x2 We have the cartesian form y=fx=x2 To convert the given equation in the polar form, Now…

Q: Find the Cartesian coordinates of the given polar coordinates. Then plot the point. (a) (-V2, 5T/4)…

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Q: Find a polar equation for x? + y² = 2

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Q: Find the Cartesian coordinates for the polar coordinates: (-V3, /6).

A: To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) : x = r × cos( θ ) y = r ×…

Q: Find two pairs of polar coordinates, one with r>0 and one with r<0,

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Q: Find a polar equation for the curve represented by the given Cartesian equation.

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Q: Find the angle α between the polar curves r1=eθ and r2=e−θ at the point of intersection.

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Q: Convert the Cartesian equation x² + y² + 3x = 0 to a polar equation. r² = = -3 cos 0 r= 3 cose r= -3…

A: Given x2+y2+3x=0To find polar equation:

Q: Convert the Polar equation to a Cartesian equation and solve for y. r2 sin(0) cos(0) +r cos(0) = 2

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Q: Find a polar equation in the form r cos (0 - 0) = ro for the line x = - 12.

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Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: 1. Change to polar form, then evaluate: -x-1 х — у dydx V1-x² /x² + y² -1

A: Solution is given below..

Q: Find the analogous polar equation for horizontal lines in the xy-plane.

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Q: Replace the Cartesian equation xy =2 with the equivalent Polar equation.

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Q: Find the slope of the polar curve r= e® at 0 = n/3.

A: Given:

Q: Find the exact length of the polar curve. = 02, 0<0 s T/2

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Q: Convert the given Cartesian equation into a polar equation. x2-y2=2x+3y

A: Given query is to convert Cartesian equation to polar equation.

Q: Find a polar equation in the form r cos (0-0) = ro for the line 2/2x+2/2 y = 16.

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Q: Assume 0 <0< T. The number of points where the two polar curves r = cos (0) and r = sin(0) intersect…

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Q: Write a polar equation of the form r cos(0 – 0,) = ro for the line x + y = v2.

A: Given line, x+y=2

Q: Find polar coordinates (r, 0) of the point, where r> 0 and 0 s0

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Q: Find the Cartesian coordinates of the point (given in polar coordinates). (1, 0)

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Q: Find a polar equation corresponding to the given rectangular equation. y= 15 1 sec(0) r= 15csc(0) r=…

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Q: Transform the rectangular equation y = - 8 to a polar equation in T and 0.

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Q: Find a polar equation for the curve represented by the given Cartesian equation. 4y? =

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Q: Convert the polar equation, r – 6r cos(0) + 9 = 16 into rectangular (Cartesian) coordinates.

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Q: snip

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Q: 2. Give the corresponding rectangular coordinates for-the given polar coordinates. 11T 7 (b) (4,3x)…

A: Given points in polar coordinates, we need to convert them into rectangular coordinates.

Q: 1. Convert from a rectangular equation to a polar equation. X-y= 10

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Q: xy = 1

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Q: Write a polar equation of the form r cos(0 – 0,) = ro for the line x - y = v2. %3D

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Q: l+vI+r² xy dydx -z 1-VT-

A: ∫01∫1-1-x21+1+x2xydydxTo transform to polar coordinates and calculate

Q: Find the polar coordinates of the point with r > 0 and 0 < 0 < 2n. (r, 0) = 0.5 1.5 2.5 3.5

A: Topic- polar coordinate

Q: Convert the polar equation r- 3 cosa 5 sin A in Cartesian equation form. )x² + y² - 3x = 5y 1- 3x =…

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Q: 1 r = sin 0-4 cos 0

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Q: Convert the point Cr,e)f from polar to nectangular COordinates (xx) 5T 3. ब्लज( कथावक 2)(a,)

A: To convert the given point from its polar form to rectangular form

Q: Convert x=3y+1 into a polar equation.

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Q: . Show that the equations x = r cos 0, y = r sin 0 transform the polar equation 1 + e cos 0 into the…

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Q: Write a polar equation of the form r sin(0 – 0,) = r, for the line x + y = v2.

A: Given given is, x+y=2 To write this line as polar equation of the form r sinθ-θ0=r0 In polar…

Q: Convert x2 + y2 = 49 to an equation in polar coordinates in terms of r and 0.

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Q: Replace the Cartesian equation with an equivalent polar equation. xy = 1

A: Consider the equation  xy=1

Q: Find a polar equation for the curve represented by the given Cartesian equation. xy = 6

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Q: Find the polar coordinates of the point with r> 0 and 0 < 0 < 2n. (r, 0) = 2 2 3 4

A: From the Figure it is clear that the value of r is 4 because it lies on the fourth circle.

Q: Find the polar equation for the curve represented by the equation y = 1+ 3x. A 1 ,0) sin 0-3 cos 0 В…

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Q: Find a polar equation for the curve represented by z +² = 8cz, where e is a constant.

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Q: Write a polar equation of the formr cos(0 – 0) = ro for the line x - V3y = 2.

A: We have to solve given problem: