Find the area of the ellipse x^2+14 x y+245 y^2=4 by using a suitable transformation that maps to the unit circle. Give an exact answer (not a calculator value).

Q: Find the equation of the circle passing through the points A(2,1), B(0,5), C(-1,2) using LU…

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Q: Describe a surface of revolution in your own words.

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Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: What is the area of the largest rectangle that can be drawn with one side along the x-axis and the…

A: given curve is y=e-x2 find the largest area of a rectangle which has one side along the x-axis and…

Q: Find the area of the region in the first quadrant that is enclosed by the coordinate axes and the…

A: Now the diagrammatic representation of the area is,

Q: Determine the area bounded by the ellipse satisfying:(101x+ 10y)2+ (20x+ 2y)2= 1.

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Q: Find the Area of the region bounded by the ellipse+ = 1?

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Q: Find an equation for the sphere centered at (1,-5, 4) with radius 4.

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Q: Rotate the ellipse =1 around the x -axis to approximate the volume of a football, as seen here.

A: To determine the volume of  that rotated about the x-axis. Given, The given curve is ellipse.…

Q: 57. Use a change of variables to prove that the area of the ellipse with equation (-) + ) : -1 is…

A: Explanation: Given that, the standard equation of the ellipse is: x2a2+y2b2=1 Solve for…

Q: Find the area of the regions enclosed by the two curves, y =x +3 and y = 4x+8. %3D

A: From the given problem:   y=x2+3 & y=4x+8       Now finding a point of intersection:…

Q: What is the relation of the conic section to the oblong plate?

A: Key Points A conic section (or simply conic) is a curve obtained as the intersection of the surface…

Q: What is the area of the conic (x + 3) + y 25

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Q: You are given a y=sqrt(36-x^2) curve that rotates about the x-axis. What is the area of the…

A: To find the surface area of rotation of the below curve about the x-axis. y=36−x2

Q: Find three different parametrizations of the graph of y = x3.

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Q: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

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Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

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Q: Find the area of the region bounded by the hyperbola 9x2 - 4y2 = 36  and the line x = 3

A: Let the graph of the area of the region bounded by the hyperbola 9x2-4y2=36  and the line x = 3 is,

Q: The area of region bounded by the parabola y2 = 4x and the line %3D y = 2x – 4 is

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4 .

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Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

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Q: 4) Use integration to find the area of the ellipse 4x² + y² = 9.

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Q: By integration, show that : 8. The area of an ellipse with semi axes a and b is A = nab.

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Q: Use disk method and draw a graph. √(9-y^2 ),y=1,y=3,x=0 about the y-axis

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Q: What is the area of ​​the region between the parabola y=x^2-1 and the line y+2x=2?

A: The solution is given below in the next step:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: The equation of the parabola is given by y = 4x2.Differentiate y = 4x2 with respect to x as follows.

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A: Given,  x=ln(2t) and y=12t2

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A: See the details solution in below

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Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

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A: The given parabola is: y=2x2 The tangent line at (5,50) has the slope: mx=5=dydxx=5          =4xx=5…

Q: h -y =

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Q: Draw the left and front vlews of the solid below. Left Front

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Q: Sketch the section of the surface at y 0. -6 -4 -2 6. -2 2 -6 -4 -6 -4 -2 -6 -4

A: The objective of the question is sketch the section of the surface at y=0.

Q: Find the volume of the solid formed if we rotate the ellipse+ = 1 about the line 4x + 3y = 20.

A: Calculation of Volume.

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = V9 - x2, 0 sxs 2,…

A: We need to find area.

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A: Hint: Here 3D points are given we need to plot them on a surface. Write the general process to plot…

Q: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: Determine the enclosed area by the curve 9x² + 25y² - 225 = 0

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Q: which satisfies th

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Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

A: We have to find the equation of the tangent plane to the hyperboloid x2-y2-z2=4 at the point 3,2,4.

Q: Find the dimensions of the rectangie of largest area that can be inscribed in the ellipse x + 256y =…

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Q: Find the area of the region bounded by the curves, y = -6, y = 6 , the y – axis and the parabola y2…

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Q: Use rectangles to estimate the area under the parabola y = x2  from 0 to 1

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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.