L0. Find parametric equation of the line perpendicular to the lines 11: x = 1-1, y=t, z= 2t -1 and 12: x =t+1, y = -t, z=1-1 at their point of intersection. Why is this line parallel to the xy-plane?

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: 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: Find the exact length of the curve described by the parametric equations. x = 5 + 6t², y = 3 + 4t³,…

A: Find the length of the curve   x= 5+t2 ,y= 3+4t2 , 0<=t<=1 .

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

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Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

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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: Find the points on the parametric curve c(t) (3t2 - 5t, t3 - 10t) where the tangent line has slope…

A: Given curve is Firstly, we find dy/dx

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Q: The lines L1 and L2 are determined by the following symmetric and parametric equations,…

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Q: 1. Graph the line using parametric equations from t = 2 tot = 6. x = 10 – 2t, y = 3 – ÷t

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Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

Q: Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t²…

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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 the equation for the line tangent to the parametric curve: t3 – 25t 25t2 – 14 at the points…

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Q: A curve is given by the parametric equations x(t)=t2-4t and y(t)=t2+2t-3. The line tangent to the…

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Q: Suppose parametric equations for the line segment between (2, a(t) 6) and (0, 0) have the form: = a…

A: Explanation of the solution is given below...

Q: Find the (perpendicular) distance from the line given by the parametric equations æ(t) 3 – 4t %3D…

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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 the equation for the line tangent to the parametric curve: t3 – 25t 25t² – t4 at the points…

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

A: This question is taken from the tangent and normal in which we have to find points on the given…

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

A: Let's find.

Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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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: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

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Q: - A curve is defined by the parametric equations x(t) = t² -4t +1 , y(t) =t³ Find the equation of…

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Q: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

A: The curve given is  x=5+3sec θy=-3+4tan θ

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

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

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Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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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: Let L1 and L2 be the lines whose parametric equations are L1 :x= -63 +9t,y = 10 – 21, z = 45 – 6t L2…

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Q: Let Lj and L2 be the lines whose parametric equations are Li :x = -10+21, y = 25 – 81, z = 17 – 6t…

A: L1 : x=-10+2t,  y=25-8t,  z=17-6tL2 : x=52-6t,  y=-43+4t,  z=20-3t

Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: Make a graph of the curve defined by the parametric equations X = t -5 on the interval 0 sts 3 y=t?

A: Given x=t-5 y=t2   0≤t≤3

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Q: List all of the points (x,y) on the parametric curve x=t^3+4t,  y=6t^2 where the tangent line is…

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Q: Q. Find parametric equation of the line perpendicular to the lines l1: x = 1- 1, y=t, 12 : z = 2t –1…

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Q: Graph the parametric curve ⟨t2−1,3t+2⟩⟨t2−1,3t+2⟩ over the interval −3≤t≤3−3≤t≤3. Identify all…

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Q: Given the parametric curve: x = t3-6t2 y = t2-4t What are all the points that the curve passes…

A: Given: the parametric curve:

Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

A: The equation of the tangent line is: y-y1=mx-x1 Where m is the slope of the tangent line. And The…

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

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Q: Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E…

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