Find parametric equations for the path of a particle tht moves along the circle x2+ (y-3)2 = 16 in the manner described. Enter your answer as a comma-separated list of equations. Let x and y be in terms of t. a) Once around clockwise, starting at (4, 3). 0 ≤ t ≤ 2?. b) Four times around counterclockwise, starting at (4, 3). 0 ≤ t ≤ 8?. c) Halfway around counterclockwise, starting at (0, 7). 0 ≤ t ≤ ?.

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

A:

Q: In each part, find an equation of the sphere with center (5, -6, –3) and satisfying the given…

A:

Q: Find parametric equation of the line segment ( L1 ) between the points P(1, 8, 9) and Q(5, 9, 18).…

A: To find the angle between two lines

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

A:

Q: In each part, find an equation of the sphere with center (5, –8, –2) and satisfying the given…

A: Given  Centre of sphere is =(5,-8,-2)

Q: I Find the Parametric equ. sor he line f intersect of Pae Plan 3X- 6y -22 =15 and 2x+Y 2Z%=5? X-3…

A: 3x-6y-2z=152x+y-2z=5a→=3, -6, -2b→=2,  1, -2a→×b→=ijk3-6-221-2a→×b→=(12+2) i^-(-6+4) j^+(3+12)…

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find parametric equations for the complete parabola x = y2. Answersare not unique.

A:

Q: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

A:

Q: Find parametric equations and a parameter interval for the motion of a particle starting at the…

A: Given,

Q: In each part, find an equation of the sphere with center (2, –3, –3) and satisfying the given…

A:

Q: Consider two non-parallel lines , l1 & l2, in R³ with parametric equations l1: P+ tu l2: Q + tv.…

A:

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1:2x – y…

A:

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: Line of intersection

Q: In each part, find an equation of the sphere with center (1, – 7, –8) and satisfying the given…

A:

Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A:

Q: Find a parmetric equation that describes the entire set of points (x,y) such that 4x2-9y2=36

A: The given curve can be represented in a different manner as shown on the whiteboard.

Q: Find parametric equations for the intersection of the surfaces y = x² and 2x² + y² + 6z² = 24 and…

A: Find out the parametric equations for the intersection of the surfaces y=x2 and 2x2+y2+6z2=24…

Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

Q: Find the point P of intersection between the line x(t) = (-3,-2, 1) + t (1, 1, -3) and the plane 4z…

A:

Q: Find a parameterization of the line formed by the intersection of the following planes: 1:2x-y+3z 1…

A:

Q: Find parametric equations for the path of a particle that moves along the circle æ² + (y – 1)² = 4…

A: As per our guidelines we are supposed to solve only one question. For the first question follow the…

Q: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: Let S be the quadric with equation 36x² – 4y? – 9z2 – 36x = 0 - - (a) Classify the graph of S. (b)…

A:

Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

A:

Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A:

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Given two points P(6,3, 1) and Q(5,0,0), find the parametric equations for a smooth curve, C:x = 5+…

A: C : x = 5 + z        y  = 3z^2

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: In each part, find an equation of the sphere with center (2, −1, −3) and satisfying the given…

A: Given that: Centre of sphere = (2, -1, -3)

Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: In each part, find an equation of the sphere with center (5, –8, –4) and satisfying the given…

A:

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: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A:

Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

A:

Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x -…

A:

Q: Find parametric equations for the line segment joining the points (-6, 7) and (4, 5). x=7-2t, y…

A:

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

A:

Q: Find the distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Q: The position in feet, of a baseball t seconds after being thrown from third base to first base is…

A: A)                                t                        x=80 t             y=-16t2+24t+5 0…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.