Find the Cartesian equation of the image of the line y = 2 under the mapping z → z 2 Sketch the image. If the pre-image point move on y = 2 from left to right, what is the orientation of the image point?

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: We make table for y=2-t   Then we make table for y=-2t

Q: Let the curve C be the mirror image of the parabola y" the line x+y + 4 = 0 If A and B are the…

A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: Find the coordinates of W. When point W lies on UV such that UV:VW is 5:2

A:

Q: Find an equation of the circle with center at (– 5, – 5) that is tangent to the y-axis in the form…

A:

Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

A:

Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

Q: Graph the line y y%3D +2 onto the coordinate plane below.

A:

Q: Find the orthogonal trajectory of the given family of curves. (x^2)+4xy+(y^2)=c

A: Given family of curve                                               x2+4xy+y2=c we have to find…

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Draw graphs of y=ex and y=1ex

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A:

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: Draw the line y = 2.x + 1 and its image under reflection in the y-axis.

A: The given line is  y=2x+1 The slope of the line is 2, Y-intercept is 1,0 and X-intercept is -0.5,0.…

Q: Find the point Q that is on the curve nearest %3D the point (4, 1)

A:

Q: Find the slope and concavity of the curve at the given points. r = 1/u, u = -pi, 1

A: Solution:Given    r=1u, u=-π,1To find the slope and concavity of the curve.Formula:Slope of the…

Q: Find the cosine of the angle between the planes x + y + z = 0 and x + 4y + 3z = 2.

A:

Q: Find the angle between the curves 4. у%3Dх and у%3х° +х-8

A: First find the intersection point of the curve then calculate slope of tangents of both the curve at…

Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Consider the given equation as x=t3....(1) And y=t2....(2)

Q: Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

A:

Q: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: Find the cosine of the angle between the planes x + y + z = 0 and x + 3y + 2z = 9.

A: Here we fnd the cosine of the angle between the planesx+y+z=0 and x+3y+2z=9

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: At what point do the curves r¡(t) = (t, 1 – t, 3 + t²) and r2(s) = (3 – s, s – 2, s²) intersect?…

A: Given Data: Curve 1: r1t=t, 1-t, 3+t2 Curve 2: r2s=3-s, s-2, s2   For the intersection point,…

Q: G) = F=, Sketch 5. Find the image rule for y = 2x + 1 given the translation t each graph on the same…

A:

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Given curves are y=2x,y=4x,y=3-x &amp; y=15x. We know that curve y=mx is equation of straight line…

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: Plot the image of point P under a translation by 4 units to the left and 3 units down.

A: coordinate of given point P(-2,-4)

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation of curve is x=t3+1,    y=t3-1,     -2≤t≤2. This implies that, x=t3+1,…

Q: Find the orthogonal trajectory of the given family of curves: 1. y = C(sec x + tan x)

A:

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: is cut by the plane given by y = the point (1, 3, -8). 3x, producing a curve in the plane. Find the…

A:

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

A:

Q: The given curve is rotated y = 3 - x2,

A:

Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

Q: ind the equation of a line tangent to the circle x2 + y2 - 8x -14y + 52 = 0 at point (7,5) a.…

A: we have the equation of circle is  x2+y2-8x-14y+52=0  .........(1) differentiate with respect to x

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A:

Q: Find the points (x, y) in the unit circle satisfying the given condition 2 b. y = - =-²/ C. x = 4y 3…

A:

Q: Give the Cartesian equation of the locus of points P(x, y) given that P is 5 units from the point…

A: Any point on the Cartesian plane is represented as x, y. The locus is a set of points on the…

Q: Find the Cartesian equation of the image of the line x = 2 under the mapping z → e z.  Sketch the…

A:

Q: Find an equation for the set of all points equidistant from the planes y = 3 and y =-1.

A: Find an equation for the set of all points equidistant from the planes y = 3 and y = -1.

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Giveny=3-t , y=-3t

Q: The domain of ƒ(x, y) = In xy is points .(x, y) in the first quadrant

A: We have to tell about given statement.

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…