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

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

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Q: Find the equation of the line tangent to the parametric curve 2t r(t) %3D t2 +1 - 0 <t<0 12 -1 y(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: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

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Q: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

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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: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: Find parametric equations of the line through (-3,0,9) that is parallel to 2i-6j+k. x(t)= 11 y(t) =…

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Q: The cartesian equation of the curve x = vt ,y= 1-t is: (a)y = 1 – x2, x 2 0 (b)y = 1 – x ,x > 0 (c)…

A: Given:-paametric equation:x=t y=1-tsince we have to find the cartesion equation

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

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Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –…

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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 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: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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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 the real number a such that the line of parametric equations x = t, y = 2 – t, z = 3 + t, te R…

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Q: z = In(x²y*) + / x² + y²

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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: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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

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Q: Complete the parametric equations for the line where the planes – 8z – 2y – 5z = 0 and - 4x + 2y –…

A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

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 a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: Which of the following is Parametric equations for the line passing through the origin and A(1, 0,…

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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

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: Which of the following is Parametric equations for the line passing through the origin and A(3, -2,…

A: We will use Standard form of parametric equation of Line passing through two points

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

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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: 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: A cartesian equation of the parametric curve x= 12t + 13 /t – 14, y = vt is OA. X = [ 3y – 2 [ 4y +…

A: We have to find the cartesian equation of the given parametric curve.

Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: Find the (perpendicular) distance from the line given by the parametric equations ¤(t) -2 – 2t y(t)…

A: Solution: The objective is to find the perpendicular distance

Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

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Q: Consider the parametric curve given by equations:  x(t)= t2 + 30t - 21 y(t)= t2 + 30t - 37  How…

A: At t = 0, determine x(t) and y(t). x0=02+300-21=0+0-21=-21   y0=02+300-37=0+0-37=-37   Thus, the…

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

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

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