17. Concentric with the circle (x – 2)² + (y – 1)² = 4 and passes through (4, –1) %3D

Q: Find the arc length of the graph by partitioning the x-axis.   9y2 = 4(1+x2)3 , from x=0 to x=4√2…

A: Given: 9y2=4(1+x2)3  from x=0 to x=4sqrt(2)

Q: 1 find the length of the curve x = 7y* + y2, from y = 1 to 24 y = 2.

A:

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

A:

Q: 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x = to…

A: If a function f(x) is defined over an interval [a,b], then the formula for arc length is: Formulae…

Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.

A:

Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

A:

Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

A:

Q: 1 Find the exact length of the curve: r(t) = , 6.

A:

Q: Find the length L of the arc formed by y=e^4x/4,0≤x≤3

A: To find the length L of the arc formed by y=e^4x/4,0≤x≤3

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: Зп 2. Find the exact length of curve y = ln (cosx), * < x < n. 4

A:

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: Find the arc length of the graph of y^2=4x^3, between points (0, 0) and (2, 4sqrt(2)).

A:

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

A:

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A:

Q: 1. The graph of y--k is shown in the xy-plane above, where & is a constant. If the arca of APOR is…

A:

Q: Find the arc length of the graph of y = √(16 − x2) over the interval [0, 4].

A: Given: y=16-x2 interval [0, 4]

Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

A:

Q: Find the arc length of the graph by partitioning the x-axis. y =2/3(x2 + 1)3/2, from x = 2 to x=7

A: The arc length of a curve y = f(x) over an interval [a, b] is given by the formula

Q: 4. Find the area of the surface generated when the given curve is revolved about the y-axis. y=(2x)"…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A:

Q: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

A:

Q: Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975…

A:

Q: 7.) Find the shortest distance between (4,2) and the curve y? = 8x.

A:

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

A:

Q: What is the area of:  To the right of Z = 0.29 and to the left of Z = -1 Show the solution and…

A:

Q: 4) Determine the equation for the shortest arc that passes through the point (0, 0) and (1, 0) and…

A:

Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

A:

Q: Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical…

A: The given line integral is ∫C2xdS where C is the arc of the parabola y=x2 from (0,0) to (1,1) and…

Q: 3/2 The length of the curve x= 4y2 from y=1 to y= 4 is given by

A:

Q: 2 4. Find the length of arc of the curve x3 + y = 1 in the first quadrant from the point where x =…

A: Let's find arc length of given curve in first quadrant.

Q: 9. Find the area of the surface generated when the given arc is revolved about the x-axis: 4x² +…

A:

Q: 9/ Find the Vale of the integrel ) Losz+Retz)r Imtz)} dz 3 is the Straitht line Segment from Zero to…

A:

Q: 4. Find the are length of the curve from y=1 to y-4

A: The given curve is x=18y4+14y-2 from y=1 to y=4

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: #4

A: Find the tangent plane to the given surface at the specified point

Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

Q: Determine the length of the arc x=ln y−(y^2)/8 for 1≤y≤2.

A: The solution are next step

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: #5. Evaluate the line integral (xydx +2x dy), where C is the arc of the parabola with equation y=…

A:

Q: 4. Find the area of the surface generated by revolving the given curve about the -axis. y = 7x,0 <…

A:

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

A:

Q: Find the length of the arc of the curve x2=(y-2)3 from P(1,3) to Q(8,6).

A:

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

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.