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

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Question 1184862: The orbit of the earth around the sun is elliptical in shape with the sun at one
focus and semimajor axis of length 185.8 million miles. If the distance of the sun from the center of the orbit is 1.58 million miles, find
a. the greatest distance from the sun to Earth, and
b. the least distance from the sun to Earth.
Click here to see answer by greenestamps(13200)

Question 1184728: An arch is in the form of a semiellipse. It is 48 ft wide at the base and has a
height of 20ft. How wide is the arch at a height of 10 ft above the base?
Click here to see answer by Alan3354(69443)

Question 1184935: what is the standard equation of Focus 10,0 and directrix: x=-10 and sketch a graph of it and what is the graph parabola of Vertex (5,-2) and Focus (7,-2)
Click here to see answer by josgarithmetic(39618)

Question 1185020: Find a quadratic function that includes the set of values below.
(0,3), (2,5), (3,−3)

Click here to see answer by greenestamps(13200)

Question 1185036: Can you help me with these? Please
Find the standard form of the equation of the hyperbola with;
1. F_1 (5,0), F_2 (-5,0)
V_1 (4,0), V_2 (-4,0)
Click here to see answer by MathLover1(20850)

Question 1185041: Find the standard form of the hyperbola with;
V_1 (-3,-3), V_2 ( 5,-3)
(asymptote : y+3 = 1/2(x-1)
Can you help me please...
Click here to see answer by greenestamps(13200)

Question 1185068: A person, standing at one focus of a whispering gallery, is 6 feet from the nearest wall. Her friend is standing at the other focus, 100 feet away.
a. What is the length of this whispering gallery?
b. How high is its elliptical ceiling at the center?

Click here to see answer by greenestamps(13200)

Question 1185067: A bridge is built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch at a distance of 40 feet from the center is to be 10 feet. Assume that the ground is the x-axis and the y-axis as the axis of the arch.
a. How high is the arch at its center approximated in two decimal places?
b. What is the horizontal length approximated to two decimal places of the arch from its axis when it’s 15 feet high?
Click here to see answer by greenestamps(13200)

Question 1185203: Hi, I hope you are doing fine. Can you help me?
A skateboard ramp is deigned to have a parabolic cross section. If the ends of the ramp should be 20 feet apart, derived the equation of its cross section using any height of your choice. What is the height of the ramp 5 feet from its center?
Click here to see answer by Alan3354(69443)

Question 1185200: An architect is requested by an investor to design a hyperboloid building.
Click here to see answer by ikleyn(52795)

Question 1185202: Hi, I hope you are doing fine. Can you help me?
The minimum width of a two-way road in the Philippines is 6.10 meters. A 500- meter tunnel is to be constructed so that its cross- section is a semi- elliptical. If the height of the tunnel should be 8 meters, what should be the maximum height of cars entering the tunnel? ( use a 0.5 meter clearance from the side of the tunnel.)
Click here to see answer by greenestamps(13200)

Question 1185249: Find the equation of the hyperbola, in general form, with vertices (±2,3) and a conjugate axis that measures 12 units.
Click here to see answer by Edwin McCravy(20056)

Question 1185250: A hyperboloid is a 3-dimensional figure whose cross section is a hyperbola. Gears that are constructed with this shape have more practical uses over the conventional gears.
Click here to see answer by ikleyn(52795)

Question 1185272: A school is building a new track for cycling teams. The track is to be elliptical,
with the ratio between the lengths of the major and minor axes to be 4:3. If the available
land is 200 yd long and 100 yd wide, what are the maximum lengths of the axes? Sketch
a graph of the track and indicate the location of the foci.

Click here to see answer by ikleyn(52795)

Question 1185283: Find the coordinates of the center, vertices, foci and equation of the asymptotes of the following hyperbolas:
a. 36x2 - 25y2 - 72x + 50y - 889 = 0
b. x2 - 4y2 - x + 12y = 0

Click here to see answer by Edwin McCravy(20056)

Question 1185453: A hyperbola with a horizontal transverse axis passes through the point (0,3). The equations of the asymptotes are y=x+1 and y=5-x. Determine the equation of the hyperbola.
My soln:
Let y=x+1 be the 1st equation, y=5-x be the second solution
Solve for x by equating equations 1 and 2
x+1=5-x
2x=4
x=2
Solve for y using eq 1
y=2+1
y=3
The center of the hyperbola is at (2,3)

Click here to see answer by greenestamps(13200)

Question 1185475: A hyperbola with a horizontal transverse axis passes through the point (0,3). The equations of the asymptotes are y=x+1 and y=5-x. Determine the equation of the hyperbola.
Click here to see answer by greenestamps(13200)

Question 1185525:
Click here to see answer by ikleyn(52795)

Question 1185526: what is the focal point of x2=-10y
Click here to see answer by ikleyn(52795)

Question 1185514: A satellite dish in the shape of a paraboloid is 10 ft across, and 4 ft deep at its vertex. How far is the receiver from the vertex, if it is placed at the focus? Round off your answer to 2 decimal places.

Click here to see answer by ikleyn(52795)

Question 1185542: The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet and 80 feet high, with the cables touching the road surface midway between the towers.
a.) Find the equation of the shape of the cable
b.) What is the height of the cable from the road at a point 150 ft from the center of the bridge
c.) Using the equation from part a, determine the total length of cable needed for the vertical sections of the cables spaced 20-foot interval.
Click here to see answer by Alan3354(69443)

Question 1185701: x^2+4x+8y+52=0

Click here to see answer by math_helper(2461)

Question 1185705: Find the equation of the circle that passes through the point (9,7) and is tangent to both x and y axis and the line 3x-4y=24
Click here to see answer by greenestamps(13200)

Question 1185816: Center at (2,-2) vertex at (7,-2) and focus (4,-2) find the equation of the ellipse
Click here to see answer by ikleyn(52795)

Question 1185835: The length of the transverse axis of the equation 100x^2-(y+3)^2=100

Click here to see answer by MathLover1(20850)

Question 1185835: The length of the transverse axis of the equation 100x^2-(y+3)^2=100

Click here to see answer by ikleyn(52795)

Question 1185766: A parabolic searchlight is 5ft across its opening. If the light source is located 2ft from the base along the axis of symmetry, how deep (in feet) should be the searchlight?
Click here to see answer by ikleyn(52795)

Question 1185687: The equation of a parabola is C is y=-2x^2+5x. The equation of line L is y-4x+1=0. a)find the intercepts of C with the axes. b) find the line of symmetry and the vertex of C. c) find the coordinates of the points of intersection of C and L algebraically. d) sketch C and L on same diagram.
Click here to see answer by Alan3354(69443)

Question 1185888: find the equation of the circle that passes through the point (9 7) and is tangent to both x and y axis and the line 3x-4y=24
Click here to see answer by Alan3354(69443)

Question 1186193: The recently made suspension bridge cables in New Bataan Hydro plant
are in the shape of a parabola. The distance between two towers supporting
the cable are 800 feet apart and the height is 200 feet. If the vertical support
cables are at 100 feet intervals along the level roadway, what are the lengths
of these vertical cables? Also write the standard form equation of an elipse.
Click here to see answer by ikleyn(52795)

Question 1186254: Vertices: (15, 1), (-1, 1); Endpoints of Conjugate Axis: (7, 7),
(7, -5)

Click here to see answer by MathLover1(20850)

Question 1186254: Vertices: (15, 1), (-1, 1); Endpoints of Conjugate Axis: (7, 7),
(7, -5)

Click here to see answer by ikleyn(52795)

Question 1186314: Vertices: (13, 0), (-1, 0); Asymptotes: 𝑦 = 𝑥 − 6 & 𝑦 = −𝑥 + 6
Click here to see answer by greenestamps(13200)

Question 1186316: Hi I need your help I'm struggling with solving this. Find the equation of the hyperbola, given vertices: (15,1), (-1,1); Endpoints of the conjugate axis: (7,7), (7,-5)
Click here to see answer by greenestamps(13200)

Question 1186364: Hello there,
I have been stuck on a math problem for hours and have no idea of how to find the solution. Please help me solve the following equation: Find an equation in standard form for the ellipse with center at the origin and passes through the points (5, 6) and (-3, 7.06).
Thank you!
-Diana
Click here to see answer by ikleyn(52795)

Question 1186493: Determine the vertex and the axis of symmetry of the given parabola. Graph your answer.
1/3 (x+3)²+1/2

Click here to see answer by josgarithmetic(39618)

Question 1186501: -4x2 + 3y2 + 24x - 12y = 36

Click here to see answer by greenestamps(13200)

Question 1186546: Two stations, located at A (-1.5, 0) and B (1.5, 0) (units are in km),
simultaneously send sound signals to a ship, with the signal travelling at the speed of 0.25 km/s. If the signal from B was received by the ship four seconds before the signal from A, find the equation of the curve containing the possible location of the ship.
Click here to see answer by ikleyn(52795)

Question 1186544: The arch of a bridge is in the shape of a semi-ellipse, with its major axis at the water level. Suppose the arch of 22 ft high in the middle, and 100 ft across its major axis. How high above the water level is the arch, at a point 30 ft from the center (horizontally)? Round off to 2 decimal places.
Click here to see answer by greenestamps(13200)

Question 1186650: Hello there,
I am currently working on a math problem that I am struggling with. Please help me solve the following problem:
Use completing the square to write the standard form of the expanded equation
10y^2-8x^2+80x+60y-190=0
___________=1
Thanks so much for your help!
-Diana
Click here to see answer by josgarithmetic(39618)

Question 1186657: Identify the center and radius of the circle with the given equation.
x^2 + (y+4)^2 - 25 = 0
Click here to see answer by ikleyn(52795)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955