Complete the parametric equations for the line wherekche planes 2=0and-2z + 2y + 2z -4 intersect. z(t) 4t: y(t) = %3D z(t)

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: Complete the parametric equations for the line where the planes - 5x – 2y + 2z = 2 and - 13x + 10y +…

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Q: 4. If y = tx, where t is the parameter, what are the parametric equations of the curve x' +y° = 4xy?…

A: The solution is given as

Q: Find the equation of the line tangent to the parametric curve (pictured below) defined by I=, y=t+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: VE is A cartesian equation of the parametric curve x = 12t + 2/t – 4, y = /t is O A. No solution…

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Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

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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: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: Q3/ Find the real number such that the line of parametric equations x = t, y = 2 - t, z= 3+t, is ax…

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Q: Find parametric equations of the normal line to * + y? at the point (2, 2, 5) the surface z= O r =…

A: In this question we have to find parametric equation of the normal line.

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

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Q: z = In(x²y*) + / x² + y²

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: 19. Find y' in the parametric equations x =, t-1 t+1 A) (f – 1) 7-1 B) (1+ 1)? 2 +1 C) (1+1)? t +1…

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Q: Consider the graph of r(t) = 2t^2i + t^2j + t^3 k Determine parametric equations of the tangent line…

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

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Q: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

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

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Q: Given the surface z = In(5x2 + 2xy - 3y2 – 12). (a) Find the equation of the tangent plane and the…

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Q: A cartesian equation of the parametric curve x = 6t + 11E - 10, y = E is O A No solution OB.…

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

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Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: For planes 2x+ y – z = 2 and 2x + 3y + 5z = 4. %3D Write the parametric equations of the line at…

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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: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

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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: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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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: Find the dx² for the plane curve with the parametric equations X = t³ – 4 and y = t2. -2 9t4 2

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Q: Eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint. 2 x2 + y2 = 36 x2…

A: We have to eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint.

Q: Let P(r, y, z) be the point at which the line with parametric equations x = -t, y=3+2t, z=1-t te R,…

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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: Calculate the dyldx at the specified point of the parametric equations of x and y : y = t? – 3t; x =…

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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: 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: A cartesian equation of the parametric curve x = 12t + 11 E - 5, y = JE is OAx = (3y – 1 ( 4y +. =…

A: x=12t+11t-5and y=tput value of t=y in x

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: 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: Eliminate the parameter in the parametric equations x(t) = –7t – 2 and y(t) = Vt – 8 to find a…

A: givenx(t)=-7t-2..................(i)y(t)=t-8..................(ii)we can rewrite 2nd equation…

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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