Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 5x² + 125y? = 125. Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-axis. Length = Width = (Type exact answers, using radicals as needed.)

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=6−x2.…

A: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=6−x2.…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

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Q: Find the largest area possible for a rectangle inscribed between the parabola y = 9 – x² and the x-…

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Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: The parabola is y=6-x2

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: Draw the parabola y=7-x^2.

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: We need to find length and width.

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 −…

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Q: = A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y -4x²…

A: Maximize area

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 –…

A: Given : A parabola, y = 9 - x²

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x. What…

A: Given that the rectangle has its base on x- axis and its upper two vertices on parabola let us take…

Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 6 –…

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Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y = 7…

A: here the width of the rectangle is  w=2x and the right is l=7-x2

Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

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

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Q: 2, i, Find out the roots of the following by completing the square. 5x^2-2x-4-0 ii, Calculate the…

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

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Q: A rectangle has its two lower corners on the xx-axis and its two upper corners on the parabola…

A: Topic:- application of derivatives

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A: The roots of a quadratics equation ax2+bx+c=0 is given by, x=-b±b2-4ac2a

Q: the length of the latus rectum of the parabola 4y=x^2-6x+21 is

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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: A rectangle has its base on the x-axis and its upper two vertices on the parabola y=6-x² What is the…

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Q: A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola…

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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: Show that,the area bounded by the parabola y^2 =4ax and a double ordinate is two third of the…

A: Let the parabola be y2=4ax Also let x =b be any double ordinate.Since the curve is symmetric about…

Q: Find the area of the enclosed by the parabola y=x2-8x+15 and the x-axis .

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Q: The area of the parabola x^2=4y-4 cut through its latus rectum is revolved about the horizontal line…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 7 –…

A: It is given that a rectangle is inscribed with its base on the x-axis and its upper corners on the…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 4 -…

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Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x2. What…

A: First draw the situation roughly

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 6 –…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 9 –…

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Q: Solve the problem. Determine the dimensions of the rectangle of largest area that can be inscribed…

A: From the figure:Let 2x be the length of the rectangle;Hence,using Pythagoras theorem;width2+2x22…

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Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here

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.