# 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x =3. Write parametric equations for C.

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: Determine A so that the curve y = 4x+ 16 can be written in parametric form as x(t) = t – 5, y(t) At…

A: Put value in given equation and simplify

Q: Find the First and Second Derivate of y with respect to x from parametric equations. x=3-t5;y=7t-5

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Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: Find the distance between the point (1, −2, 4) and the line given by the set of parametric equations…

A: The given point is M=(1, −2, 4) The direction vector of the line is =s=(2,1,2) A point on the line…

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

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Q: 7. Sketch the curve with parametric equations z =e, y =e', teR.

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Q: Find the First and Second Derivate of y with respect to x from parametric equations. a). x=(t-2)5/2…

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

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² + ¹/² = 4…

A: We need to obtain a set of parametric equations for the curve of intersections of the cylinders:…

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: What is the Cartesian form of the parametric equations.x(1) =t+ 4 and y(t) = t² + 31 + 1? Provide…

A: To eliminate the parameter.

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

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Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: iminate the parameter in the parametric equations x(f) = 5t – 8 and y(t) = Vt – 5 to find a…

A: Given: The parametric equations are xt=5t-8 and yt=t-5 Given query is to find the Cartesian…

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

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

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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: Find a set of parametric equations for the curve of intersection of the given paraboloid and plane:…

A: Solution:-

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

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Q: Find the 1st  and 2nd Derivate of y with respect to x from parametric equations.     x=(t-2)5/2…

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

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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: 18. Find the acute angle between the plane x+2y-z=8 and the line with parametric equations x =1, y…

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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: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x² and the top half of…

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Q: iminate the parameter in x = -t +2t and y =t-4 and then identify the parametric sketch its image in…

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

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Q: What is the Cartesian form of the parametric equations x(t) = 4t – 2 and y(t) = /t – 3? %3D Provide…

A: To find cartesian form of equation

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 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: 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 parametric equations for the line tangent to the curve of intersection of the surfaces tan-1(x?…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

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: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

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Q: Sketch the plane curve represented by the parametric equations x = Vi and y = }t + 1 by eliminating…

A: The parametric equations are given by x=t   …1 and y=12t+1   …2 Take the square of the equation (1)…

Q: Complete the parametric equations for the line wherekche planes 2=0and-2z + 2y + 2z -4 intersect.…

A: The equation of the planes are: P1: 2z = 0 ⇒ z = 0                                  .........1 P2:…

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.

A:

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.