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Q: a Show that y = mx + b intersects y = |x + 1| if m > 1 or m < -1. b Given that -1 < m < 1, find the…

A: Given,y = mx + cFor m &gt; 1Take  m = 2 &gt; 1,

Q: Consider the curve defined by x =t – 4 and y =t² + 3, for -3 <t < 4. Find an equation in X and Y…

A: Solved follow step below.

Q: Let C be the curve y = x³ – 3x2 + 4x - 1 joining the points (1, 1) and (2, 3). Find the value of |…

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Q: Let C C R? be the path from (3, –2) to (3, 2) along the graph of the curve x – 5x?y? – 7x2 = 0.…

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Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

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Q: a) [ i) Find the exact length of the curve y = x³ + 12x 1≤x≤2

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Q: If the length of the curve y = 3 x7 from the point (0, 0) to the point (xo, f(xo)) is L = 8 , then…

A: Length of curve

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

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Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

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Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Find the length of the curve r=θ^2 from θ=0 to θ=6

A: Given: -

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Consider the line L(t) = (3t – 1,3 + 2t). Then L intersects: 1. The x-axis at the point when t = 2.…

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Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: Find the exact length of the curve.   y2 = 4(x + 4)3 , 0 ≤ x≤ 2 , y&gt; 0

A: Given: y2=4x+43,0≤x≤2,y&gt;0 To Find: Find the Exact length of the curve. Concept: Length of the…

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

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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 the length of the curve y = x2 from x = 0 to x = 7.

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Q: The length of the curve y = from x = 0 to x 6 is

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Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

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Q: d the exact length of the curve. y = 1 + 8x3/2, Osxs1

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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: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

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Q: For curve r = (t, t2,t-³) %3D Does this curve go through the point (-1, 1, -1)?

A: We have to find if the given curve passes through the point (-1,1,-1).

Q: The cartesian equation of the curve x = VE ,y = 1-t is: (a)y = 1-x2, x20 (b)y = 1-x ,x20 %3D (c) x =…

A: Cartesian equation is a equation which involves x and y , just I have eliminate the t from given…

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

A: The given curve is in paramatric form as following- x=√t y=1-t Where t is a parameter. To find the…

Q: Consider the curve defined by x = 2t – 1 and Y = 2 – t, for –5 <t< 3. Find an equation in X and Y…

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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: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line a + y = -1 at the point…

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Q: The cartesian equation of the curve x = vE .y 1-t is: (a)y = 1- x2, x 2 0 (b)y = 1-x ,x 20 (c) x =…

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Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A…

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1)…

Q: Find the points on the curve y-9x closest to the point (0, 4). ) and (O

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Q: Q22. determine the family of curves that is orthogonal to the family Zy²+3x²=X when z > O and yea.…

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Q: Q1. Find the length of the of the curve y = from x = 0 to x = 3.

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Q: Find the length of the curve of y=x³/2 from x=1 to x=4.

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Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

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Q: n of the curve, L. (x+ 1)* , 0 0

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Q: trace the path of the curve f(t) = (3e', 4e24)

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Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: The length of the curve y from x=0 to x= 6 is

A: We need to find the length of the curve  y=23(x2+1)32 from x=0 to x=6

Q: Q1. Find the length of the of the curve y= from x = 0 to x = 3.

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.