Find a Cartesian equation for the curve represented by polar equation r= 14 cos - 6 sin e. OA. 2 (x – 7)° + (y +3) = 58 OB. 2 (x- 7)° + (y +3) = 20 OC. 2 (x-7)° + (y +3) = 9 OD. 2 (x- 7)* + (y +3) = 49 OE. (*+7)* + (y-3)' = s +(-3)' = = 58

Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and - the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Find the slope of the tangent line to the polar curve r=2−sin(theta) at the point specified by…

A: To find the slope of tangent line.

Q: Find the slope of the line tangent to the polar curve at the given point. 9 11t r= 9 sin 0; 2' 6

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Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 < 0 <…

A: To convert Cartesian equation into polar equation , put x=rcosθ, y=rsinθ in y=3x3 ⇒rsinθ=3 ×rcosθ3…

Q: Find the exact length of the polar curve described by: 9e -0 on the interval

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Q: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

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: Find the points at which the polar curve, r = 4 cos θ , has horizontal and vertical tangent lines.

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

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Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

A:

Q: Find a Cartesian equation from the polar curve 4r sin 0 = 18(rcos 0) +14 1S is

A: Given polar equation is 4rsinθ=18rcosθ2+14  .....1

Q: Find the slope of the polar curve r = 2( 1 – cosx ) when x = pi/4 . a. 1.707 b. 2.414 c. 1.866 d.…

A: Given equation of curve : r=21-cosx   ,  x=π4. drdx=2sinx The slope of polar curve   r=21-cosx  at…

Q: Find the slope of the line tangent to the polar curve at the given points. 7-49 cos26. (0.7). (0.-)…

A: Slope of the tangent line at given point for curve r2=49cos2θ

Q: 3. Consider the curves given by the polar equations r = 2 and r = 4 cos 0.

A: r = 2 r = 4 cosϴ

Q: Determine the points at which the limacon defined by the polar equation r = 3+ 2 sin 0 has…

A:

Q: A particle moves along the polar curve r = -4+ 4 sin 0 in such a way that the angle between the…

A: r = -4+4sinθ  dθ/dt= 5 unit/sec  Find dr/dt when θ = π/2

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Let The slope of the tangent line is given as,  Differentiate r with respect to

Q: Given the curve in polar equation r = 8 cos 0, 0<0 Use integration to find the area of surface…

A: Given the curve in polar equationr=8 cos θ, 0≤θ≤π2.By using the integration to find the area of…

Q: Sketch the curve with the given polar equation, and find its Cartesian equation. 1 1-cos e

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 9 cos(8) 2

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Q: Find the slope of the line tangent to the polar curve at the given points. r=3cos2(theta); at the…

A:

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A:

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: We use the slope of the tangent line of a curve y=f(x) to answer the given question.

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: Polar curve is

Q: Find a polar equation for the curve represented by the given Cartesian equation. x^2 + y^2 = 6x −…

A: Given equation is : x2 +y2 = 6x -4y Concept : To convert an equation in polar form, we substitue x =…

Q: The slope of the tangent to the polar curve r 2 sin(0) at 0 = is O- V3 None of these 1 V3 V3 1 V3…

A:

Q: Find dy/dr and the slopes of the tang ent lines shown on the graph of the polar equation r = 2+3 sin…

A: According to question, r = 2 + 3 sin θ

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A:

Q: Find the equation of the line tangent to the polar curve at the point. r= 2cos(θ/ 3),  θ =π/4

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Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

A:

Q: Find an equation in x and y that has the same graph as the polar equation r-sin e =0 and graph on…

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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…

A:

Q: Find the points at which the polar curve r= 5+ 10 sin 0 has a horizontal or a vertical tangent line.…

A: the equation of the given curve in polar form is: r=5+10sinθ we have to find the points to the curve…

Q: Find the equation in xx and yy for the line tangent to the curve in polar coordinates…

A: Given that, the value of r=5+cos2θ and θ=π3. rθθ=π3=5+cos2π3=5+-12=92 Note that, the equation of the…

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: Sketch the curve with the given polar equation, and find its Cartesian equation. 2 =-4 sin 20 %3D y

A: We are given the polar equation . Let us plot the figure.

Q: Find the slope of the polar curve at the indicated point. r = 1 - sin θ, θ = 0

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A:

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve is,

Q: 8. Find the equation (in terms of Cartesian variables r and y) of the tangent line to the polar…

A: Given curve is Firstly, we find slope of tangent to polar curve is

Q: 4. a) Express the given rectangular equation in polar form. Solve for r or r2 if possible. x? = y? +…

A: Use x= rcostheta Y= r sin theta X2+y2=r2

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 0…

A: Given: r=3+5 cosθ We have to sketch the graph of r as a function of θ in Cartesian coordinates…

Q: 15) Find the slope of the tangent line to the given polar curve at the point specified by the value…

A:

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A:

Q: The graph of the polar equation r(0) = 0 cos(0), o ses. with derivative = cos(e) – 0 sin(0), is…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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.