Find three additional polar representations of the point, using -2n < 0 < 2n. (Enter your answers in order from smallest to largest first by r-value, then by 0-value.) (r, 8) = (r, 8) = (r, 8) = (

Q: Q3: Find and classify all fixed points and plot the portrait on a circle for the system è = 2 + 2…

A: Given equation is θ.=2+2cosθ. We have to find the fixed points of the given system. Then we will use…

Q: Q2 Q1 Find the points of intersection of the polar curves r-cos 0 = 0 and 2-cos-r=0

A:

Q: Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

Q: Select a parametric equation that represents the line that passes through the points (3,0,−2) and…

A: Find the direction vector of the line using the two points

Q: Suppose parametric equations for the line segment between (-2, 8) and (7,3) have the form: a + bt…

A: This question can be solved by substituting the values of x,y and t in the given equations.

Q: Graph the line and conic section. r = 8/(1 - sin u)

A: We can convert this into rectangular form. Then,…

Q: 33. Find parametric equations for the path of a particle that moves along the circle x² + (y – 1)² =…

A: from the equation of a circle given to us, we have the radius r = 2 as the general form of the…

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x - 5 between…

A: formula:

Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: The parametric equations for x3+y/3-4 , when 0s0<2n are:

A: See the attachment

Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

A:

Q: 4. Endpoints of its conjugate axis at (0,-3) and (0,3) and one focus at (5,0)

A: Given that endpoints of its conjugate axis at (0,-3) and (0,3) and focus at (5,0). We need to find…

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: Evaluate the by itercated integreal onverzting to polare coordinates. V16-n² 3nd ydn V16-パ 16-42 -4

A: This integration problem is solved by converting rectangular coordinate into polar coordinate

Q: 2. Find the parametric equations of the line passing through the point (-1,4, -3) and is parallel to…

A:

Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+2t y%3Dt z-5-3t -o<…

A:

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: 2. Find the symmetric and parametric equations of the line containing the point A(1,2, 1) and x-2…

A:

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Is the given statement true or false? Justify your answer. 10 3-2 cos 0 is a = 13. Directrix of a…

A: The given polar equation is r=103-2cosθ. Rewrite it as follows.

Q: 5. Find the parametric equation of the line passing in R³ passing through the points (3, 1,0) and…

A: Directly use the formula for the parametric equation in R3

Q: i HW/ O change from. polar to Cartesian Co-ovdinate's (3, ) vE-2- Cose ... 1,0) © (-4, 3), @ (5,…

A:

Q: 4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to…

A: From given equations, we find sin theta and cos theta Then we plug them in the Pythagorean identity…

Q: 6. Find the image equation of the line -2x +y + 3 = 0 under the rotation about C = (1, 1) at an…

A:

Q: Find parametric equations for the line segment starting at P(3, –4) and ending at Q(-5,2).

A: We have to find the parametric equation of the given line.

Q: 8) Find the parametric equation of the Line passes through p (2 -4,5) parallel 19to 3x+y-97 =5 and…

A: This question can be solved using the concepts: general equation of a line condition of  line and…

Q: Find the points of horizontal and vertical tangency (if any) to the polar curve. r = 3 tan θ

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

A:

Q: Which of the following is Parametric equations for the line passing through the origin and A(3, -2,…

A: We will use Standard form of parametric equation of Line passing through two points

Q: Find the parametric equation of the line that passes through the point (4, -5, 0) and is…

A: We have to find the parametric  equation of the line.

Q: 30. Determine two sets of parametric equations for the line passing through the points P( 1,7, 1)…

A:

Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: (2. Plot the points with polar coordinates 2, and -3, 2 using the pencil. 6. 3 3n 4 5n 6. 4. 7n 6.…

A: topic - plotting of points in polar coordinate system

Q: Consider the polar curve r=2sin(30) for 0s0sn.

A: Given polar curve is r=2sin3θ for 0≤θ≤πfind the area of the region inside the curve

Q: Find parametric equations for the line segment thatgoes from Q(0, 3) to P(-2, 0).

A: Given Q(0,3) and P(-2,0)

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

Q: 3. Write down the name of the conic given by the polar curve r = 6/(2-sine). Determine the vertices…

A: Given problem:- 3Write down the name of the conic given by the polar curve r = 6/(2-sin(θ))…

Q: 2. Graph the following parametric equations on XY plane. Select a set of t-values. x=r+5 y=1-?

A:

Q: Calculate the length of the polar curve r=1- sin Oon the given interval (0, 2m].-

A:

Q: 3. Write down the name of the conic given by the polar curve r = 6/ (2 - sine). Determine the…

A:

Q: y+3x-6z=8

A: answer is in next step

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: (iii) 3rd subplot is A butterfly curve using polar coordinates: 2a - I r = esina – cos(4a) - sin( 24…

A: (iii) Matlab Code: clc; clear all; close all; theta= 0 : pi/32 : 8 * pi; r= e.^…

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: polar Co-ovdina 4x²= y²-44+8

A:

Q: Find a set of parametric equations for the line segment from (-1,5) to (9,–4).

A:

Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?

A:

Q: 3. Transform x^2+y^2-2x+y-2=0 from rectangular to polar

A: The given rectangular equation is: x2+y2-2x+y-2=0