Find parametric equations for the line segment from  (9, 2, 1) to (5, 5, −1).  (Use the parameter t.) (x(t), y(t), z(t)) =

Q: B- Find the parametric equations for the line through point (1,0) and parallel to the function f(x,…

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Q: x = t + t and y = t* + 2t²

A: If the parametric equation of a curve are x=f(t) and y=g(t), then the slope of the tangent line at…

Q: Eliminate the parameter from the parametric equations to find the rectangular equation for the…

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Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: Find the Cartesian equation of a curve defined parametrically by 5t and y = 10t for all real values…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Sketch the curve defined by the parametric equations x = t2, y = t + 1, -∞ < t < ∞.

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Q: 12- Find an equation of the tangent plane to the given parametric surface at the specified point.…

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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: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

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Q: Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t),y = 2…

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Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: Which is a parametric equation for the curve y = 9 – OA. c(t) = (t, 2 + t) OB. c(t) = (t, 9 – 2t)…

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Q: Find the Cartesian equation of a curve defined parametrically by 5t and y =10t for all real values…

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Q: x = 2t2 – C : 3t + 1 y = et²-1

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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 x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

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Q: 2. Find the parametric equations of the tangent line to the curve as result of the intersection of…

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Q: Find a parametric equation for the path of a particle that moves halfway around the circle…

A: We have to find the parametric equation for the path of a particle.

Q: Find the points on the parametric curve c(t) = (3t^2 -3t, t^3 -6t) where the tangent line has slope…

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Q: Find the exact length of the parametric curve x =1+3t², y = 4+2r°, 0<t<2.

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Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = t + 4, y =…

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Q: Find the length of the curve defined by the parametric equations 3 -t, y = 3 In((t/4)? – 1) x = 4…

A: Given:- x =(3t/4)  y = 3ln((t/4)2-1)  To find:- Length of curve from t =5 to t=6

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: Find a parametric representation of the solution set of the linear equation.x + y + z = 1

A: Consider the given linear equation  x + y + z = 1 We have one equation and three unknown(x, y, z).…

Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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

A: We have to find parametric equation for the line that is perpendicular to the graph of the given…

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +…

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

A: Let's find.

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

A: Equation of line normal to graph of functions f(x) is :  r&lt;t&gt; = &lt;x0,y0,z0&gt; +…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: Find the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

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Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

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Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

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Q: ) Suppose that the parametric equations x = 1, y = r', 12 0, model the position of a moving object…

A: Given

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

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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: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

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

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Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: Find the equation of the tangent line(s) to the given set of parametric equations x = t² + 5t – 6 y…

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Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

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Q: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

Q: find parametric equations for the given curve. 4x − y2 = 5

A: Given curve is:

Q: A curve in the plane is defined parametrically by the equations written below. An equation of the…

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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.