Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x + y+ z = 2 and perpendicular to the line x = 1+t, y = 5 – t, z = 5t . 1. x = 3 – 6t, y= 6+4t, z = 4 +t %3|

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

A: We have to find

Q: Consider the parametrically defined curve x = 6sin(3t), y = t, z = 6cos(3t); (0, T, – 6) %D Find the…

A: The normal plane is orthogonal to the tangent vector r ' ( t )  Let vector equation of curve is r (…

Q: Find parametric equations for the line through (7,4, – 7) perpendicular to the plane 4x + 5y + 4z =…

A:

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: Suppose parametric equations for the line segment between (1,9) and (0, Sx(t) = a + bt ly(t) = c+ dt…

A:

Q: The parametric equation of the line through the points (2, –4,1), (2, –4,1) and (0,4, –10) is: A. x…

A:

Q: Find parametric equations for the line through Po= (3, -1, 1) perpendicular to the plane 3x + 5 y -…

A: Given:  a Point Po =(3, -1, 1)  and a vector perpendicular to the plane is…

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

A:

Q: Find parametric equations of the normal line to x2 the surface z + y? 4 at the point (2, 3, 10)

A:

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

A:

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

A:

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

A:

Q: Suppose parametric equations for the line segment between (7, 3) and (3, 0) have the form: S z(t) =…

A:

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

A:

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: 2. Find parametric equations for the line tangent to the curve of intersection of the surfaces at…

A:

Q: 9. Given the parametric equations x = et and y = te-t, vt. dy (a) Find dx (b) Find dx2 d?y (c) For…

A:

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

A:

Q: Find parametric equations of the normal line to x² the surface z = + y? 4 at the point (2, -3, 10)

A: Given curve

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

A:

Q: Given the planes  π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Let L be the line of…

A:

Q: List all of the points (x,y on the parcmetric curve X= +?+ 4+ y= 6+3 where the tangent line is…

A:

Q: 2. Find the point(s) of intersection of the following two parametric curves, by first eliminating…

A: From x=t+5 we get t=x-5 Then we plug this in the y=t2 So, the equation is: y=(x-5)2   We can plug…

Q: 7. The curve at right is given by the parametric equations t2 z = v2t. x = In t, y = Find its length…

A: Given that, x=lnt,y=t22 and z=2t. That is, r→t=lnt,t22 ,2t. It is known that, the length of the…

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

A: Here we have to find the equation of the tangent line.

Q: Suppose parametric equations for the line segment between (7, 8) and (5, 1) have the form: Sx(t) = a…

A: We have to find

Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x-1+3t y=t z35+2t -<…

A: Two points A and B are given we have to find the parametric equation of the line segment AB. A line…

Q: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

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Q: 3. Find the equations of the normal plane and the osculating plane to the curve at the given point…

A:

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

A:

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: Suppose parametric equations for the line segment between (2, 8) and (– 2, 0) have the for s ¤(t) =…

A:

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

A:

Q: Find parametric equations for the line through (- 4,6,1) perpendicular to the plane 7x + 3y + 9z =…

A: Note that, a vector which is perpendicular to the plane ax+by+cz+d=0 is (a, b, c). A parametric…

Q: Find the equation of the plane that passes through the point (2, 1, 1) and is tangent to the surface…

A: We have to find the equation of the tangent plane.

Q: Suppose parametric equations for the line segment between (2,4) and (−2,2) have the form: x(t)=a+bt…

A:

Q: Find parametric equations for the line through (- 3,1,2) perpendicular to the plane 7x + 9y + 9z =…

A:

Q: Suppose parametric equations for the line segment between (4, 3) and (– 1, – 10) have the form:…

A:

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

A:

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

A: Consider, r(t)=lnt4i+t-4t+8j+t lnt4kWe first evaluate r(t) at t=t0=4r(4)=ln44i+4-44+8j+4 ln44k…

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

A:

Q: Consider the equation of the surface S given by x2z2 + xy + yz = 7. An equation for the plane…

A: First differentiate at given point then use equation of tangent plane

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

A: A detailed solution is given below.

Q: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

A:

Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

A: Topic - equation of line

Q: 2 The parametric equations of a curve are y = 2 sinnt, t, x= 2+ 2t – 2 cost. 10 10 Find the area…

A: We have been given parametric equations of a curve and we have to find the area under the curve.

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.