I have twp questions  1.What is the largest area of a rectangle that could be inscribed in a semi circle having a radius of 15m.   The other one is   1. An ellipse has an equation of 225x2+400y2=90000. What is the maximum area of a rectangle that can be inscribed in the ellipse?

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4 – x². What…

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Q: What is the equation of a parabola with vertex at (0,0), opens to the left and the length of latus…

A: Explanation: Given that,  Vertex of the parabola is (0,0) and the length of the Latus Rectum is 6…

Q: What is the nearest distance from the point P(6,0) to the parabola? y^2=8x

A: GivenP(6.0)y2=8x To find nearest distance

Q: A one-way road passes under an overpass in the shape of half an ellipse, 25 ft high at the center…

A: given: A one way road passes under an overpass in the shape of half an ellipse, 25 ft high at the…

Q: What is the length of the minor axis of the ellipse 4x² + 32x + y² – 4y + 52 = 0? 0 4/3 0 4 0 8 O 45

A: Topic = Ellipse

Q: The parabola y = x² – 1 is constructed, but the axes are gone, somehow! With the help of ruler and…

A: Let us consider the function y=f(x) The transformation will shift the graph as  If y=f(x)+c and…

Q: Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes,…

A: Let 2x and 2y be the length and width of rectangle with sides parallel to the coordinate axes, that…

Q: Find the equation of the hyperbola with center (o, o), a vertex at (5, o) and an extremity at (o,…

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Q: 20. Find the ratio of the length of minor axis to the length of the major axis of the ellipse 9x^2 +…

A: Given that: 20.9x2+16y2-144=021.y=x(x+1)3 22. Area of rhombus=24 sq. units. One diagonal=6 units.…

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

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Q: A ship is following a course that is 104 miles from and parallel to a straight coastline. The ship…

A: Given: Let A represent the location of origin. As a result, its coordinate is (0,0). Because the…

Q: A certain bridge arch is in the shape of half an ellipse 148 feet wide and 32.1 feet high. At what…

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Q: Find the dimensions of the largest rectangle that can be inscribed in the ellipse 9x² + 16y² = 144.…

A: 9x2+16y2=1449x2144+16y2144=1x216+y29=1x242+y232=1it is in the form of ellipse…

Q: Consider the point P (-1,0)on the ellipse 4x2 + y? What is the value of a? Answer to 3 significant…

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Q: 1. Find the dimensions of the rectangle of maximum area, with sides parallel to the -1 16 coordinate…

A: Given ellipse is  x2144+y216=1 We need to find the dimensions of the rectangle of maximum area with…

Q: Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed…

A: Let the dimension of such a rectangle be 2x by 2y. Clearly (x, y) is point on the ellipse.

Q: A geometry student wants to draw a rectangle inscribed in the ellipse x2+4y2=16x2+4y2=16. What is…

A: Let A=the area of the rectangle x=half the base of the rectangle So, A=2x·216-x22;0≤x≤4   =2x16-x2…

Q: Find the equation of the horizontal ellipse that is centered at ( 27 , 18), passes through the point…

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Q: 3. Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes…

A: Let vertex of the rectangle be x,y, x,-y, -x,y and -x,-y. Thus, are of the rectangle is fx,y=4xy. We…

Q: A rectangle with sides parallel to the coordinate axes is inscribed in an ellipse (Figure 12a)…

A: Let the length of the rectangle is = 2x  Let the height of the rectangle=2y (as shown in the…

Q: A geometry student wants to draw a rectangle inscribed in the ellipse x2+4y2=49. What is the area of…

A: For maximization, equate the derivative of the function to 0 to get the critical points.Then check…

Q: Jim and Bob want to exchange secrets from across a crowded whispering gallery. (A whispering gallery…

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Q: What is the maximum area of a rectangle inscribed in the ellipse 25 + y? = 1?

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Q: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the…

A: The arch can be modeled by the vertex form of a parabola centered at the origin with the base being…

Q: Find the length of the diameter of the ellipse 3x2+y2 +2x-6y=0. Which has a slope of 2.

A: Ellipse

Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

Q: Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that…

A: Given equation 2x2+72y2=72which can be writtenx236+y21=1

Q: Find the dimensions of a rectangle with a maximum perimeter that can be inscribed in the ellipse 4x…

A: Given ellipse 4x2+9y2=36                ->Equation(1)Let (x,y) be the upper right corner of the…

Q: A landscape architect is designing an elliptical pool that will fit in the center of a 20-by-30-…

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Q: A geometry teacher wants to draw a rectangle inscribed in the ellipse x? + 4y² = 16. What is the…

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Q: Show the figure or model of a rectangular object 25 m wide is to pass under a parabolic arch that…

A: given that Parabolic arch has a width 32m at the base and height 24m at the center Vertex of…

Q: A rectangle is inscribed with its base on the ?x-axis and its upper corners on the parabola y=2−x^2.…

A: Given, The equation of the parabola is y=2-x2

Q: The parabola y=x^2y=x2y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.…

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Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: 5. FIND THE MAXIMUM AREA ENCLOSED BY A RECTANGLE WITH PERIMETER OF 84 FEET, 6. WRITE…

A: If perimeter is known we have to find maximum area Here I am giving solution of first question if…

Q: An isosceles triangle with vertex at (0, -1) is to be inscribed in the ellipse x² + 4y2 = 4. Find…

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Q: 3. Find the dimensions and area of the largest rectangle having its two lower corners on the x- axis…

A: The given problem is solved below in detail.

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

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Q: Given the ellipse x^2/16+ y^2/4=1. What is the area of the largest rectangle that can be cut from…

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Q: 10. Find the area of the largest rectangle that can be inscribed in the ellipse 16x2 + 36y² = 576.

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Q: A rectangle is inscribed in an ellipse so that two of its sides pass through the foci. If the x2…

A: The distance between foci of an ellipse x2a2+y2b2=1 is 2ae Where, e=1-b2a2 (a>b)

Q: The area and perimeter of the given ellipse are given by the equations 2n va? +b2 with 0 < a < V2…

A: Given  Area=abπ Perimeter=2πa2+b22 0≤a≤2 0≤b≤2   Perimeter of the ellipse fixed at a value of 2π ft

Q: One of St. Matthew's Hall is 10 feet wide and has a semi- ellipse ceiling. The ceiling is 6 feet…

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Q: Find the dimension of the rectangle of maximum area that can be inscribed in the ellipse…

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Q: A cable durpended between two Do po has a Jag of 1. 20 meters apart a form of a parabola, find its…

A: The distance between the pole = 20 m and the sag of 112 m=32 m. We have to find the equation of the…

Q: (x-3)? (y+1)² = 1? 16 25

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Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed in the ellipse x2/a2…

A: Let 2x,2y be the length and width of the ellipse that is inscribed in ellipse  Then , perimeter of…

Q: Find the envelope of the family of ellipses x2/a2+y2/b2=1 having the same area.

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Q: A rectangle is to be inscribed in the ellipse described by x? + = 1. What should the dimensions of…

A: Given,  The equation of the ellipse x2 + y29 = 1  We have to find the dimension of rectangle with…

Q: Find the equation of the horizontal ellipse that is centered at ( 27,18), passes through the point (…

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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.