At the center of the lobby of a hotel is an artificial pond in the shape of an octagon serving as an elegant master piece. At a designated time, water fountains would appear at the vertices and the center of the octagonal pond. If the distance between consecutive spouts is 1.5 meters, what is the area occupied by the pond?

Q: A searchlight is shape like a parabola of a revolution. If the light source is located 2 feet from…

A: Given that , vertex of parabola h,k=0,0 focus of parabola 0,a=0,2 Depth of light y=4 feet Width of…

Q: The equation of the Family of Parabolas with vertex (h,-3) and it opens to the left is

A: We use the equation of the parabola when open the left and vertex are (h,k) is (y-k)2=4a(x-h)

Q: 3. The towers supporting the cable of a suspension bridge are 1200 m apart and 170 m above the…

A: Solution:-   First we are draw a rough diagram based on the given problem.      Both towers are…

Q: ht

A: Introduction: We know that the equation of the parabola in the vertex-focus form with coordinates…

Q: Given 4 points on a vertical ellipse (-1.366, 0), (0, 2.241), (1, -12), and (4, 2.43).  Select the…

A:

Q: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

A: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

Q: The equation of the parabola which opens up, vertex (-3, 4), and the length of latus rectum is 8…

A: Given that 8)  parabola open up with vertex (-3,4) and length of latus rectum is 8 9)  the parabola…

Q: The distance between foci of an ellipse is 6 and its major axis is 10, find the length of the latus…

A:

Q: find the maximum area of a rectangle inscribed in an ellipse whose equation is 4x^2+25y^2=100

A: Solution: 4x^2+25y^2=100 The equation is divided by 100 4x2100+25y2100=100100x225+y24=1 or…

Q: Write the standard form of the equation of the parabola that has the indicated vertex and pa Vertex:…

A:

Q: Find the area of the largest rectangle that can be inscribed in the ellipse b2

A:

Q: An artist bends a long plank of wood into the shape of a parabola. The horizontal distance between…

A:

Q: The vertical line passing through the vertex of a parabola is called the ......... .

A: Given The vertical line passing through the vertex of a parabola is called the ......... .

Q: A cable suspended between two posts that are of the same height and 20 meters apart has a sag of 1/2…

A: Given: A cable suspended between two posts that are of the same height and 20 meters apart has a…

Q: .כ Find the ared of a parabola which is inscribed in a rectangle 40 cm long and 25 cm wide.

A: We know are of parabola is( 2/3) ×b×h Where b is base of parabola and h is height of parabola.

Q: Find the vertices and foci of the ellipse: 49x2 + 9y2 = 441(Round to the nearest tenth if…

A: For the standard form of ellipse x2a2+y2b2=1, vertices will be ±a, 0 or (0, ±b) as per a>b or…

Q: The outer door of an airplane hangar is in the shape of a parabola. The door is 140 inches across at…

A:

Q: how many side does a hypercube have?

A: using definition from online,

Q: Show that an ellipse has exactly 4 vertices, unless it is a circle.

A: Consider an equation of ellipse x2a2+y2b2=1 where a,b>0. In parametric form, its equation can be…

Q: The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable…

A:

Q: The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints…

A: Given:The line segment perpendicular to the axis of symmetry, passing through the focus and with…

Q: Your dog is hyper and needs to go for a walk around the block. If your block is rectangular and the…

A: Solution ) walk around the rectangular block = perimeter of rectangle perimeter of rectangle = 2 ( a…

Q: 2. is the width of the track 15 a from esther vertex? A jogging path is in the shape of an ellipse.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

A:

Q: Find the length, breadth of the rectangular box of maximum area that can be inscribed in the ellipse…

A: The area of a rectangle is Area=Length × Breadth The area is maximum if the second derivative of…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse x2 1. b2 +

A:

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

A:

Q: A pair of buildings on a college campus are shaped and positioned like a portion of branches of the…

A:

Q: The vertex of a parabola is (-5, 2), and its focus is (-1, 2). What is the standard form of the…

A:

Q: Correctly match up the vertex and axis of symmetry for this parabola.

A: We have to find the vertex and axis of symmetry according to the given information

Q: What is the opening, focus, directrix, axis of symmetry, and endpoints of the latus rectum of the…

A:

Q: ow that, the equation 3x -y + 5x – 2 = 0 repr ngent at the vertex, directrix, latus rectum, len…

A:

Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: Why is distance between vertices for hyperbola equal to 2a?

A:

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5), and…

A:

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: What are the vertex and the axis of symmetry of the parabola shown in the diagram below?

A: follow next step

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 towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280 meters apart…

A: The parabola is a u-shaped graph of a quadratic function. The general equation of a parabola is…

Q: How is the distance between vertices for hyperbola equal to 2a?

A:

Q: The towers supporting the cable of a suspension bridge are 1200 m apart and 170 m above the bridge…

A: Cable is 116 meters high at 120 meters away from the tower. Answer and explanation is given below

Q: What is the length of the latus rectum of the parabola: y2 – 4y – 8x – 28 = 0?

A: Given, y2 – 4y – 8x – 28 = 0 General equation of parabola with center (h,k) (y-k)2=4a(x-h)    ---(i)

Q: If we have a parabola with an axis of symmetry of x = 9 and it contains the point (-3, -12), what…

A: Given taht parabola is symmetric about the line x= 9

Q: What is the length of the transverse axis of the hyperbola whose foci are (0, -5) and (0,5) , and…

A: The foci of Hyperbola are:   (0, -5)  and  (0, 5). Length of transverse axis of Hyperbola is:  2a…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse  x2/a2 + y2/b2 = 1.

A: Let (x,y) be a vertex of rectangle. Then, length of rectangle = 2x, width = 2y. Then area of…

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 260 meters.…

A:

Q: Find the vertex and length of the latus rectum for the parabola. y = (x - 2)2 - 9 Vertex: (x, y) = (…

A: Topic = Parabola

Q: Find the area of the largest rectangle that can be inscribed in the ellipse 1.

A: To find the area of the largest rectangle

Q: A parabolically shaped bookshelf has a width of 14 feet 8 inches at the top and height 8 ft. 4 in..…

A: Consider the given information as, width=14feet  8 inches and height =8ft 4 in