Questions on Algebra: Conic sections - ellipse, parabola, hyperbola answered by real tutors!

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Question 1091687: A street with two lanes, each 10 ft wide, goes through a semicircular tunnel with radius 12 ft. How high is the tunnel at the edge of each lane? Round off to 2 decimal places
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Question 1091792: Parabola
A satellite dish has a shape of paraboloid. The signals that it receives is reflected to the receiver that is located at the focus of the paraboloid. If dish is 8 feet across at its opening and 1 foot deep at its vertex, determine the location (distance from the vertex of the dish) of its focus.
Please help. Thank you
Click here to see answer by josgarithmetic(39618)

Question 1091906: A parabolic arch is constructed which is 8 ft wide at the base and 9 feet tall. Find the height of the arch exactly 1 foot in from the base of the arch

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Question 1091797: Parabola
A fountain in a shopping mall has two parabolic arcs of water intersecting in one point. The equation of one parabola is y= -0.25x^2+2x and the equation of the second parabola is y= -0.25x^2+4.5x. How high above the base of the fountain do the parabolas intersect?
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Question 1091795: Parabola
The Lovell Telescope is a radio telescope located at the Jodrell Bank Observatory in Cheshire, England. The dish of the telescope has the shape of paraboloid with diameter of 250 feet. The distance from the vertex of the dish to its focus is 75 feet.
A. Find an equation of a cross section of the paraboloid that passes through the vertex of the paraboloid. Assume that the dish has its vertex at (0,0) and vertical axis of symmetry.
B. Find the depth of the dish. Round to the nearest foot
Click here to see answer by ikleyn(52795)

Question 1091793: Parabola
The antenna of a radio telescope is paraboloid measuring 81 feet across with depth of 16 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna.
Please help. Thank you
Click here to see answer by ikleyn(52795)

Question 1091794: During televised football games, a parabolic microphone is used to capture sounds. The shield of the microphone is paraboloid with diameter of 18.75 inches and a depth of 3.66 inches. To pick-up the sounds, a microphone place at the focus of the paraboloid. How far (to the nearest tenth in inch) from the vertex of paraboloid should the microphone be placed?
Please help. Thank you
Click here to see answer by ikleyn(52795)

Question 1092086: If the points (2,3) and (3,2) on a parabola are equidistant from the focus,then find the slope of its tangent at vertex?
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Question 1089210: The vertex of the parabola (x-y+1)^2=4*(x+y-5) is?

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Question 1089210: The vertex of the parabola (x-y+1)^2=4*(x+y-5) is?

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Question 1092085: If the point (2a,a) lies inside the parabola x�-2x-4y+3=0 then find a lies in the interval?
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Question 1092125: Rewrite the relation as a conic in standard form, then sketch the graph of the relation.

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Question 1092157: Find the equation of the cus of the point if its distance from R(-4,1) is always one-half its distance from E(3,2)
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Question 1092156: Find the equation of the locus of the point if its distance from L(2,1) is always twice its distance from S(-1,3)
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Question 1092187: The circle below is centered at (4, -1) and has a radius of 3. What is its equation?
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Question 1092186: For which values of a does the conic
2x^2 + 5y^2 − 30y + 8x = a
have at least one point? (Enter your answer using interval notation.)
Click here to see answer by Alan3354(69443)

Question 1092181: a satellite dish has a shape called paraboloid where each cross section is a parabola since ratio signals (parallel to the x-axis will bounce off the surface of the dish to the focus the receiver should be placed at the focus.How far should the receiver be from the vertex if the dish is 12 ft across and 4.5 ft deep at the vertex?
Click here to see answer by greenestamps(13200)

Question 1092207: C(7,4) is internally tangent to x^2+y^2+12x-8y+3=0. Find the equation of the circle.
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Question 1092209: C(23,-1), internally tangent to x^2+y^2-34x-14y+313=0. FIND THE EQUATION OF THE CIRCLE ( This is a harder case, please answer w/ complete solution)
Click here to see answer by KMST(5328)

Question 1092228: An archway that is above a highway is in the shape of a semi-ellipse 60 ft wide and 25 ft high. How high is the archway 10 ft away from the center ?
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Question 1092271: Identify the conic section in 4x2+4y2+40x+16y+40=0 in standard form

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Question 1092271: Identify the conic section in 4x2+4y2+40x+16y+40=0 in standard form

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Question 1092269: y2-8y+12x-8=0 what is the focus , directrix and the endpoints of latus rectum

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Question 1092488: All parabolas with vertex on the line 2x-y=0, and with axis parallel to the y-axis.
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Question 1092452: The path of aship can be described by a hyperbolic model centered at the origin, relative to two stations on the shore 168 miles apart that are located at the foci. If the ship is 60 miles south of the center of the hyperbola, find the equation of the hyperbola.

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Question 1092594: Find an equation of an ellipse having a vertex at (3,7) and foci at (3,-1) and (3,5).
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Question 1092965: Find the equation of ellipse with centre (1, 4),vertex at (1,7) and eccentricity e= 2/3. sketch the graph.

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Question 1093415: 8x^2-9y^2-40x+4y+145=0
Show what type of conic section this is, and write its equation in standard form.
Click here to see answer by Alan3354(69443)

Question 1094135: find the equation of two circles which pass through point (2, 0) that have both Y-axis and the line y-1 =0 as the tangent.
am sorry to asked this question but I need your help.
thank
Click here to see answer by greenestamps(13200)

Question 1094383: Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix
y = 9.
PLEASE ANSWER FAST AND SHOW ALL WORK!! THANK YOU SO MUCH IN ADVANCE :)
Click here to see answer by josgarithmetic(39618)

Question 1094384: A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base.
Find an equation for the parabola if the vertex is put at the origin of the coordinate system.
Please show all work because I'm super confused. Thank you so much! :)

Click here to see answer by Alan3354(69443)

Question 1094665: Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4.

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Question 1094664: Find the center, vertices, and foci of the ellipse with equation x^2/400 + y^2/256 = 1.

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Question 1094797: Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4.
help
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Question 1095275: Pls help me solve : given the with equation 25x^2+16y^2=400 .find the i) length of the major axis,ii)the length of the minor axis,iii) eccentricity, iv)coordinate of the foci,v) coordinates of the vertices,vi) the coordinate of the directrices,vii)the latus rectum of the ellipse.

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Question 1096065: Find the equation of the circle which passes through points a(0,2), b(2,0) and c(-4,0)
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Question 1096051: for the ellipse x^2/a^2 + y^2/b^2=1 with foci at (-c,0) and (c,0), show that b^2 = a^2 � c^2
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Question 1096474: A parabola has focus (7,9) and directrix of y=3. Find its standard equation
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Question 1096703: Determine whether a quadratic model exists for the set of values below. If so, write the model.
f(0)=1, f(3)=-20,f(-1)=-4
Thank you,
Click here to see answer by Alan3354(69443)

Question 1096936: An equilateral triangle ABC circumscribes the circle with equation x^2 + y^2 = a^2. The side BC of the triangle has equation x=-1
a) Find the equations of AR and AC.
b) Find the equation of the circle circumscribing triangle ABC.
Click here to see answer by greenestamps(13200)

Question 1097151: Write the equation of the circle having radius 2.5 and tangent to the line 2y=x at (2,-3)
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Question 1097745: Find a function p(x) for an arch that is 15 feet tall and 16 feet wide at the base
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