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

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Question 1186656: Identify the center and radius of the circle with the given equations.
x^2 + y^2 + 8y -9 = 0
Click here to see answer by ikleyn(52795)

Question 1186658: An ellipse has vertices (2 − √ 61, 5) and (2 + √ 61, 5), and its minor axis is 12 units long. Find its standard equation and its foci.

Click here to see answer by MathLover1(20850)

Question 1186623: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft apart. If the bridge is tangent to the cables at its center, find the length of one of its vertical support 30 ft from one of the towers.
Click here to see answer by ankor@dixie-net.com(22740)

Question 1186713: Find the equation of hyperbola, foci at (3,5) and (3,-5), length of transverse axis is 6.
Click here to see answer by MathLover1(20850)

Question 1186882: center at the origin; a focus (0,2); vertex at (0,3)
Click here to see answer by ikleyn(52795)

Question 1186881: What is the equation of the ellipse having major axis of length 12, center at
(-2,-9), and a focus at (3,-9)?
Click here to see answer by Edwin McCravy(20056)

Question 1186992: What is the standard form of 5x^2 + 30x = -24y + 72
Click here to see answer by josgarithmetic(39618)

Question 1187043: FIND THE EQUATION OF THE PARABOLA WITH VERTICAL AXIS THAT PASSES THROUGH THE POINT (0,2) AND THE POINTS OF INTERSECTION OF THE PARABOLAS x² + 2x + 3y + 4 = 0 AND x² - 3x+ y + 3 = 0.
Click here to see answer by josgarithmetic(39618)

Question 1187080: FIND THE EQUATION OF THE PARABOLA WITH VERTICAL AXIS THAT PASSES THROUGH THE POINT (0,2) AND THE POINTS OF INTERSECTION OF THE PARABOLAS x² + 2x + 3y + 4 = 0 AND x²- 3x + y+ 3 = 0.
Click here to see answer by MathLover1(20850)

Question 1187079: find equation for the parabola with vertical symmetry axis and containing the three points (0,2), (1/2, -9/4), and (5, -63).
Click here to see answer by josgarithmetic(39618)

Question 1187159: Write the equation of the hyperbola given the following information Vertices : (2, - 6); (- 4, - 6) Foci: (- 1 + sqrt(10), - 6), (- 1 - sqrt(10), - 6)

Click here to see answer by MathLover1(20850)

Question 1187285: On a grid map of a province, the coordinates that correspond to the location of cellular phone tower is (-7, 4) and it can transmit signals up to a 12 km radius. What is the equation that represents the transmission boundaries of the tower? Is the household located at (5, -8) within the transmission boundaries?
(1) Given
(2) Required to find
(3) Graph/Illustration
(4) Equation to be used
(5) Computation
(6) Final answer

Click here to see answer by Alan3354(69443)

Question 1187288: It has been shown that when like particles with a common charge are hurled at each other, they deflect and travel along paths that are hyperbolic. Suppose the path of two such particles is modeled by the hyperbola x2-9y2= 36. What is the minimum distance between the particles as they approach each other? Assume x and y are in microns.
(1) Given
(2) Required to find
(3) Graph/Illustration
(4) Equation to be used
(5) Computation
(6) Final answer

Click here to see answer by Alan3354(69443)

Question 1187366: y=x^2+24x-60
Find the vertex form
Click here to see answer by josgarithmetic(39618)

Question 1187286: Sound technicians at professional sports events often use parabolic receivers as they move along sidelines. If two -dimensional cross section of the receiver is modeled by the equation y2= 55x and is 36 inches in diameter, how deep is the parabolic receiver? What is the location of the focus?
(1) Given
(2) Required to find
(3) Graph/Illustration
(4) Equation to be used
(5) Computation
(6) Final answer

Click here to see answer by KMST(5328)

Question 1187287: As part of an art show, a gallery owner asks a student from a university to design a unique exhibit that will highlight one of the more significant pieces in the collection, an ancient sculpture. The student decides to create an elliptical showroom with reflective wall, with a rotating laser light on a stand at one focus, and the sculpture placed at the other focus on a stand of equal height. The laser light then points continually at the sculpture as it rotates. If the elliptical room is 24 feet long and 16 feet wide, how far from the center of the ellipse should the stands be located (round to the nearest tenth of a foot). How far apart are the stands?
(1) Given
(2) Required to find
(3) Graph/Illustration
(4) Equation to be used
(5) Computation
(6) Final answer

Click here to see answer by KMST(5328)

Question 1187425: Give the coordinates of the foci, vertices, and co-vertices of the ellipse with equation
(x²/169) + (y²/25) = 1. Sketch the graph and include these points.
Click here to see answer by ikleyn(52795)

Question 1187453: Please help me with this. foci (-2, 3) and (4, 3) b=4. This is only the problem the teacher gave us. This is all about ellipse

Click here to see answer by MathLover1(20850)

Question 1187463: Find the equation of the locus of a point which moves so that the sum of its distances from the points (2,1) and (8,1) is 10

Click here to see answer by ikleyn(52795)

Question 1187462: foci (-2, 3) and (4, 3) b=4
Please help me solve this. Find the general and standard form then graph it. If it is not that much of a hassle, i would also appreciate it so much if it has a solution. This is all about ellipse. This is the equation that i ended up with

Click here to see answer by MathLover1(20850)

Question 1187471: find th equation of the ellipse determined by the given conditions vertices (0,0) and (0,8), focus (0,1)
Click here to see answer by greenestamps(13200)

Question 1187461: find the equation of the parabola determined by the given condition: axis vertical and passing through (0,0), (1,0), and (5,-20)
Click here to see answer by ikleyn(52795)

Question 1187479: What is the degenerate conic sections of
9x²-4y²+18x-16y=7
3x²+5y²-6x-20y=-25
Click here to see answer by Alan3354(69443)

Question 1187496: 1. During the old normal, regular admission for a movie ticket is Php 160 per ticket
while the seniors pay Php 140 per ticket. If the total sales for a certain movie is
Php 29, 600 for an audience of 190 people, how many seniors watch the movie?
How many are not seniors?
Click here to see answer by ikleyn(52795)

Question 1187578: FIND THE EQUATION OF THE PARABOLA:
Axis vertical and passing through (0,0) , (1,0) and (5,-20)
the equation pls thank you so much:)
Click here to see answer by MathLover1(20850)

Question 1187578: FIND THE EQUATION OF THE PARABOLA:
Axis vertical and passing through (0,0) , (1,0) and (5,-20)
the equation pls thank you so much:)
Click here to see answer by ikleyn(52795)

Question 1187587: Reduce into standard equation of the hyperbola. 25x²-50x-9y²-36y-236=0
Click here to see answer by greenestamps(13200)

Question 1187596: Find the tangent line of the function f(x) =16x − 4√x at x = 4, and the point at which tangent line and the x-axis meets.

Click here to see answer by Alan3354(69443)

Question 1187618: As part of an art show, a gallery owner asks a student from a university to design a unique exhibit that will highlight one of the more significant pieces in the collection, an ancient sculpture. The student decides to create an elliptical showroom with reflective wall, with a rotating laser light on a stand at one focus, and the sculpture placed at the other focus on a stand of equal height. The laser light then points continually at the sculpture as it rotates. If the elliptical room is 24 feet long and 16 feet wide, how far from the center of the ellipse should the stands be located (round to the nearest tenth of a foot). How far apart are the stands?
Click here to see answer by ikleyn(52795)

Question 1187647: find the equation of a parabola with vertex on the line y=2x, axis parallel to the x-axis and passing through (3/2, 1) and (3,4).

Click here to see answer by greenestamps(13200)

Question 1187712: find the equation of the parabola
axis vertical and passing through (0,0),(1,0), and (5,-20)
note: do not use the equation y= ax^2+bx+c
Click here to see answer by josgarithmetic(39618)

Question 1187711: what is the equation of the parabola axis vertical and passing through (0,0), (1,0), and (5,-20)
Click here to see answer by josgarithmetic(39618)

Question 1187727:
Click here to see answer by josgarithmetic(39618)

Question 1187729: can I ask this for last time, it's just that the other answer is correct but will use another equation.
axis vertical and passing through (0,0),(1,0),(5,-20)
using the equation: (x-h)^2=-4a(y-k)
thank you so much, sorry for the inconvenience
Click here to see answer by josgarithmetic(39618)

Question 1187731: I beg you, please help meeee
Find the equation of the parabola determined by the given conditions
Axis vertical and passing through (0,0)(1,0)(5,-20) using equation (x-h)^2=-4a(y-k)
NOTE: I beg you to please strictly use (x-h)^2=-4a(y-k) as the equation as you solve this
Click here to see answer by josgarithmetic(39618)

Question 1187732: Find the equation of the parabola determined by the given conditions
Axis vertical and passing through (0,0)(1,0)(5,-20) using equation (x-h)^2=-4a(y-k)
NOTE: Strictly use (x-h)^2=-4a(y-k) as the equation as you solve this
Click here to see answer by josgarithmetic(39618)

Question 1187756: Find the equation of parabola with the given condition:
Axis vertical and passing through (0,0)(1,0) and (5,-20)
Note: Do not use y=ax^2+bx+c as the equation
Use: (x-h)^2=-4a(y-k)
Can you also show me the solution? Ty
Click here to see answer by Edwin McCravy(20056)

Question 1187759: Hello
Find the equation of the parabola determined by the given equations.
Axis vertical, vertex (-1,-1), and passing through (2,2).
Note: Please strictly use (x-h)^2=4c(y-k) as the equation
Click here to see answer by josgarithmetic(39618)

Question 1187847: Write the equation of the circle centered at (−7,−2) that passes through (13,−15).

Click here to see answer by josgarithmetic(39618)

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