x = Vi, y = 3t + 4;

Q: 4x2 Trace the curve y? %3D (x+5)(x-2)

A: Given function is y2=4x2x+5x-2  ....1

Q: find a cartesian equation for the curve r2 = 14

A: Find a cartesian equation for the curve         r2 = 14

Q: Find the equation of a circle whose center is at (4,2) and tangent to the circle x² + y? – 8x – 6y+…

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Q: i) Find the cartesian coordinate of the point P(r, 0) = (-3, ). Plot the graph

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Q: Q2/ By using polar coordinate, graph the curve r=1-2cos 0.

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Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

A: a. According to question,Given equation,y = 1-x2 ,  z = -2

Q: (d) Find the points on the curve x'y = 60 nearest the origin.

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Q: Find a Cartesian equation for the curve and identify it. r2 = 14

A: We have to find Cartesian equation

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: Find the exact length of the curve 36y? (x² – 4)³, 2 0.

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Q: On the grid below, sketch a curve that satisfies the following conditions: НА: у- 1 x-intercepts: 0…

A: First we draw asymptotes x=+2,x=-2, y=1.

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

A: Parametrization is a way to change the parameters of a expression in such a way that domain of the…

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

A: Find the equation in terms of x by substituting x=t in the given expression   y=t2-1=x2-1   To use…

Q: 2. Find the exact length of the curve. y = 3 ,1 < x< 2 15+51

A: Find the exact length

Q: Find the point (a, b) on the graph of y = e^x where the value ab is as small as possible.

A: Solution:Given y=exTo find(a,b)  where ab is as small as possible.

Q: (a) Eliminate the parameter to find the Cartesian equation of the curve. (b) Sketch the curve and…

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Q: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

Q: Q 3. Find the equation of (i) A circle passing through the points (2, 1), (0, 2) and (1,0).

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Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

Q: Determine the equation of the directrix of the curve 3x=2y2-4y+7 (Graph Solution) a. x=30/20…

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Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x 1+2nx b) y = =

A: Get  the asymptote of equation in a: y=limx→∞x2e-x   =0 Thus, plot the graph:

Q: Find the coefficients a, b, c, and d so that the curve shown in the accompanying figure is the graph…

A: The equation is given as y = ax3+bx2+cx+d                               (1) The point (1,7) must…

Q: Which of the following point (æ, y) on the graph of y = /2x is the nearest to the point (4,0) ?…

A: 1. The parametric form of equation Y2= 4aX is X = at2 and Y= 2at. 2. The perpendicular distance from…

Q: Find a Cartesian equation for the curve and identify it. r2 = 10

A: Given, We have a polar equation  r2 = 10

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 expression for x and y is given by  x = t - 2  and  y = 2t+3 The range of t is 0≤t≤5 t = x…

Q: Find the equation of a circle whose center is at (4, 1) and tangent to the circle x² + y? – 8x - 6y…

A: standard equation of circle (X-h)2 +(Y-k)2 = r2 center (h,k) , radius = r    Here circles touches…

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

A: To find the equation in terms of x and y from the parametric equations x=ft and y=gt, we have to…

Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. x=t°…

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Q: In the figure above, the value on the y-axis decreases as we move from Select one: O a. point C to…

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Q: Solve the problem. Find the length of the curve y = In(csc x), 7/4 T/2 VI E

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Q: Starting with the graph of y = e x  write the equation of thegraph that results from(a) reflecting…

A: (a) Plot the curve y and reflect the graph for y about y = 0 axis.

Q: Please help

A: To determine the largest possible value of |r|.

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

A: We have given the curve x=et ,y=e-t ,t∈ℝ.We have to find an equation in x,y whose graph contains the…

Q: XXI. Determine the equation of a circle whose center is at (4, 5) and tangent to the circle whose…

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Q: i. x = sin (y – 5) ii. -3x2 + y z2 = 6

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

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: The equation x2 + y2 + Dx + Ey + F = 0 is called the_________ form of the equation of a circle.

A: The general form of the equation of a circle is x2+y2+Dx+Ey+F=0. D, E and F are constants.

Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. x=t-1…

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Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. x- Vt,…

A: Given x=t, y=3t-2 for t in 0, 4

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

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

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Q: r= g° ,0<g<\5

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Q: Find the coefficients a, b, c, and d so that the curve shown in the accompanying figure is the graph…

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Q: Find the coefficients a, b, c, and d so that the curve 20 shown in the accompanying figure is the…

A: Given y = ax3+bx2+cx+d                           (1) The point (0,10) satisfies the equation (1) ,…

Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem