What is the parametric equation for the line through the point (1,2, 3) paralkel to the y- axis? (a) x = 1+ 2t, y = 0, z = 0 (c) x = 0, y = 1 + 3t,z = 0 (b) x = 0, y = 2 + 5t, y = 0, z = 0 (d) a, b, & c

Q: Find parametric equations for the line passing through the points (10,3,1) and (8,6,-2) using the…

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Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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

A: Use the given planes.

Q: Find a set of parametric equation of the line through the point (-2, 0, 3) parallel to the vector v…

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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: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

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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: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: What is the parametric equations of line line through the point (1,2,-1)and is perpendicular to the…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: Find a set of parametric equations for the line passing through the point (8, 0, 9) that is parallel…

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Q: 4. Determine the parametric equation of the line that passes through (2, -1, 3) and is perpendicular…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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Q: A particle moves in space along a path whose parametric equations are given by bsin(wt), x2 =…

A: Image is attached with detailed solution.

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: The objective is to find the parametric equations of the line through the point.

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

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

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Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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Q: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

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Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: Find the parametric equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

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Q: What are the parametric equations of x - 2y + 3z - 1 = 0?

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve). x…

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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)…

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

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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: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

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

A: The solution is given as follows

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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

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Q: What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y =…

A: 7) The Parametric equations of the line through (2, 2, 2)  parallel to x-axis is given…

Q: (3) Find parametric equations for the line of intersection of the planes. x + y - z = 2 and y + z =…

A: Given equation of the planes are  x+y-z=2     y+z=0 we rewrite them as x+y-z-2=0, and    0x+y+z=0…

Q: Find a set of parametric equations for the line passing through the point       (1, 0, 2) that is…

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Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: <3, 1, 1> +…

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

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Q: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1:   x−2y+z=1P2:   2x−2y−4z=4

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.