5. Convert the given functions into the desired coordinates. (a) 2x-5x³=1+xy into polar coordinates, (b) r=-8cos(0) into cartesian coordinates.

Q: A particle a of mass m moves inside a bowl. If the surface of the bowl is given by the equation Z m…

A: As per the question we are given the 3d equation of a surface in cartesian coordinates as :  z =…

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

A:

Q: Match the given parametric equations with one of the parametric curves. x=3- sint, y=3+ cost

A: It is given that x=3-sint, y=3+cost. we have to find the graph of the parametric curve

Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: Find the points of horizontal and vertical tangency to the polar curve               r = 1 − sin

A: Consider the given polar curve: Here the objective is to find the point of horizontal and vertical…

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

A:

Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

A:

Q: 4. Integrate L e-° dxdy by converting to polar coordinates, and ase that result to integrate J e dx.

A: This problem is convert to pollar form and then solve so,......

Q: Sketch the curve with polar equation r = 2 cos0

A: We first make a table of values θ 0 π/4 π/2 3π/4 π r 2 1.41 0 -1.41 -2

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

A:

Q: Find a polar equation for the curve represented by x2 + y2 = 8cx, where c is a constant.

A: The given equation is x2 + y2 = 8cx   Known fact x=rcosθy=rsinθ

Q: 1. Change ſ, Lz xy dydx to polar form. 4-x2

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 9. Sketch the polar curve. r = 2 cos 2 0

A:

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

A:

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A:

Q: 01: If x²+y-2x=0. Find the corresponding equation in polar. Sketch.

A:

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A:

Q: 2. \ Evaluate •V4-2² dydx + dydx 2x-r2 using polar coordinates.

A: We have to evaluate the integral using polar coordinates.

Q: 9. Sketch the polar curve.r= 2 cos 2 0 ||

A:

Q: Match the given parametric equations with one of the parametric curves. x= 2- sint, y= 2 + cost

A: To determine the parametric curve for given equation.

Q: 5(a) Find the slope of the tangent line to the polar curve r = 2sin0 -3cos0+1 at 0= 1/4

A: Using slope formula we have

Q: Q2 Find the points of intersection of the polar curves r=1+cos 9 and r= -cos

A: Point of intersection of the Polar curve

Q: Find the exact length of the polar curve described by: r = 2e-0 on the interval 7 6" π ≤ 0 ≤ 9π.

A:

Q: Q5/ Change the polar equation 2r = 2 + cos 0.(2r-1) to Cartesian equation Ans./y²-3x² - 4x-1=0

A: To find- Change the polar equation 2r = 2 + cosθ·2r - 1 to Cartesian equation.

Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

A:

Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: 8 Convert the polar equation r 2 = -2 sin 2θ to a Cartesian equation. x2 + y2 = 2 xy ( x2 + y2) 2…

A:

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

A:

Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: 1. Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0< 27, to find the area…

A:

Q: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y…

A:

Q: 1. Transform the polar equation 4 cos 0 cos² 0 + 1 into its Cartesian form and identify the curve.

A:

Q: Sketch the polar curves r= 9 sin 0 and r 4-9 sin 0. Indicate the co- ordinates of all r and y…

A:

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: Consider the curve C of equation: (x² + 2y + y²)² = 4(x² + y²). From the following options choose…

A:

Q: d) Find the slope of the parametric equations x=2+3sin and y=0-cose at 0=

A: Given: x=2+3cosθ and y=θ-cosθ   As we know that; The slope of the tangent line to the given curve is…

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

A:

Q: cos (0.48-j0.38) express in polar form

A: we have to express cos 0.48-j0.38 in polar form: we know that cosx-jy=cosxcoshy+jsinxsinhy Now, here…

Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: Example 7 Sketch the curves (c) r 0 (0 > 0) in polar coordinates.

A:

Q: 2. Evaluate Vr2 + y? dy dx by switching to polar coordinates.

A:

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

A: