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

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A: 41. Here the given as  Now we let

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A:

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

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

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A: Find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

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

Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

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Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: Find two different sets of parametric equations for y = x2 + 6.

A: Our Aim is to find the two different sets of parametric equations for y=x2+6

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: Find parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

A:

Q: Can someone help me out with this question?

A: On a horizontal line, the y value is fixed.  And x values are changing.

Q: Find the set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

Q: Write three different sets of parametric equations for the curve $y=\sqrt{x}$

A:

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

A: Given,

Q: Eliminate the parameter t from the parametric equationsx = 3+1 2 sec t and y =2+  4 tan t.

A: Given parametric equations are x=3+12 sect and y=2+4 tant We have to eliminate the parameter t from…

Q: Find parametric equations for the line through P = (2, 5) perpendicular to the line y = 4x − 3.

A: Given line, y = 4x − 3. To find the parametric equations for the line through (2,5) and…

Q: Sketch the curve with parametric equationsx = 3t − 4, y = 3 + t^3

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Q: A particle is moving along the curve given by the parametric equations x=1+t, y=1−t. Determine the…

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Q: In an open space, Thomas throws a ball at an angle of 70° to the horizontal with an initial velocity…

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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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: Eliminate the parameter of the pair of parametric equations. x = 3t, y = t + 7 O y = 3x + 7 O y = 3x…

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Q: Find the length of the curve defined by the parametric equations

A: Given parametric equations are x=(5/6) t and y=5 ln((t/6)2-1) from t=7 to 9 W need to find length of…

Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

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Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) =…

A: This is the answer of question no. 4.

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: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

A: Given: x2+y2=25; -3,4 for finding equation of line that is perpendicular to given curve at given…

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line (x-4) = 2…

A: The solution is given below in the next step:

Q: I need to get the parametric equation for a line between the points (0,1,2) to (3,0,-1). I have the…

A: Line passing though the points 0, 1, 2 & 3, 0, -1. Now let, x0, y0, z0=0, 1, 2 & x1, y1,…

Q: 6. Find the distance between the point (- 3, 2, 1) and the line with parametric equations x = 3 –…

A: Consider a point on the line (3-2t, 1-t, -3t) which is the foot of the perpendicular to the point…

Q: Find the slope of the line whose parametric equations are x=4t+6 and y=t-1

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Q: What are the direction numbers of a line given by the parametric equation:  x=6+t,y=5+4t,z=1−2t

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Q: Find the corresponding Cartesian equation of the parametric equation       x=3cosθx=3cosθ.…

A: Given:           x=3 cos θ,   y=4 sin θ            0≤θ≤2π From: x= 3 cos θ            cos θ=x3 From:…

Q: Draw the curve given by the parametric equationsx=t3+t2−t,y=t3+2t2−4t.

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

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

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Q: Find a set of parametric equations for the rectangular equation that s y = 2x – 3, t = 0 at the…

A: let x = t + a put all the given points to find out the value if a x = 4 and t = 0 4 = 0 + a a = 4 so…

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

Q: Under what circumstances can a graph that represents a set of parametric equations have more than…

A: On considering the parametric equations x=f(t) ----(1) y=g(t)----(2) Where, x and y is a function…

Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.