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

Tutors Answer Your Questions about Quadratic-relations-and-conic-sections (FREE)

Question 1067893: The reflecting surface of a parabolic antenna has the shape formed when the parabola is rotated about its axis of symmetry. If the measurements are in feet, how far from the vertex should the receiver be placed if it is to be at the focus?
I am having a hard time solving this problem. I do not understand the question, any sort of assistance would be greatly appreciated!
Click here to see answer by ikleyn(52799)

Question 1067892: A parabola has its vertex at (-2,1) and its focus at (-2,-1). Write the equations of the parabola, the directrix, and the axis of symmetry. Graph the parabola.
Click here to see answer by josgarithmetic(39620)

Question 1068076: What is the equation of hyperbola whose foci are (-2,-1) and (-2,9) and whose transverse axis has length 8 is?
Click here to see answer by josgarithmetic(39620)

Question 1068142: Write the equation of an ellipse with vertices (0, 12) and (0, -12) and co-vertices (2, 0) and (-2, 0).
Click here to see answer by ikleyn(52799)

Question 1068141: Write the equation of an ellipse with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2).

Click here to see answer by ikleyn(52799)

Question 1068269: find the equation of the ellipse which passes through (2,4)and (1,5).
Click here to see answer by ikleyn(52799)

Question 1068144: Write the equation of a hyperbola with vertices at (-3, 0) and (3, 0) and co-vertices (0, 5) and (0, -5).
Click here to see answer by KMST(5328)

Question 1068143: Write the equation of a hyperbola with vertices at (1,1) and (9, 1) and foci at (0, 1) and (10, 1).
Click here to see answer by KMST(5328)

Question 1068563: Find the length of the major axis.
(x - 8)^2/49+(y+6)^2/121=1

Click here to see answer by stanbon(75887)

Question 1068640: Centered at (0,0) passing through (-3 , 3.35) and (-1.5, 0)
Click here to see answer by ikleyn(52799)

Question 1068649: A bridge over a railroad is supported by a parabolic arch. The clearance from the base to the top of the arch must be 40 metres. The inside distance between the supports is 120 metres. Write an equation that describes the arch. Show your graph.
Click here to see answer by Fombitz(32388)

Question 1068652: I've got two LORAN stations A and B that are 500 miles apart. A and B are also the Foci of a hyperbola. A ship at point P (which lies on the hyperbola branch with A as the focus) receives a nav signal from station A 2640 micro-sec before it receives from B. If the signal travels 980 ft/microsecond, how far away is P from A and B? Also, what are the values for a, b, and c? Show your illustration.
Click here to see answer by rothauserc(4718)

Question 1068651: A tunnel is built under a river for a road 12 m. wide with a 2m. sidewalk on either side. The top of the tunnel is semi-elliptical. A local law stipulates that there must be a clearance of at least 3.6 m. at all points on the road. If the smallest possible ellipse is used, find the clearance at the center of the road. Show your illustrations.
Click here to see answer by Fombitz(32388)

Question 1069252: drawing the largest triangle in side a parabola graph defined by f(x)=8-x^divided by 2

Click here to see answer by Alan3354(69443)

Question 1069405: How do I find the vertex and focus and directrix of y=1/2x^2
Click here to see answer by josgarithmetic(39620)

Question 1069496: Identify the type of conic section whose equation is given and find the vertices and foci.
1) x^2=y+1
2) 4x^2+4x+y^2=0
Click here to see answer by Fombitz(32388)

Question 1069667: A circular vent pipe with a diameter of 5.6 inches is placed on a roof that has a slope of 1.1/1. The intersection of the vent pipe and the roof is an ellipse. What is the equation of the ellipse, with all values being written up to the 4th decimal place?
Click here to see answer by ikleyn(52799)

Question 1070292: Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis vertical with length 16; length of minor axis = 6; center (0, 0)
Click here to see answer by ikleyn(52799)

Question 1070453: Find the center (h,k) and radius r of the circle and then use these to (a) graph the circle and (b) find the intercepts, if any.
40x^2+40x+40y^2=0
Click here to see answer by josgarithmetic(39620)

Question 1070553: So, I have the answer to this problem, I just don't know how to get to it --> Find the equation of the ellipse with center at the origin, x-intercepts at (+-2,0) that passes through the point ( -1, ((sqrt15)/(4)) ).
Click here to see answer by Fombitz(32388)

Question 1070725: what is the vertex of -x^2+2x-7

Click here to see answer by Fombitz(32388)

Question 1070725: what is the vertex of -x^2+2x-7

Click here to see answer by MathTherapy(10552)

Question 1070725: what is the vertex of -x^2+2x-7

Click here to see answer by Alan3354(69443)

Question 1070859: Equation of a circle whose end points of the diameter are x+y = 4 and x - y = 2, and passing through (2,-1)
Click here to see answer by ikleyn(52799)

Question 1071015: In my math class, we are working on factoring and solving for x. I have understood most of the problems, but this one has really stumped me.
m(squared) - 10m = 0
Could you please help me?
Click here to see answer by josgarithmetic(39620)

Question 1071339: Please explain how you do this question: Derive the equation of the locus of a point P(x,y) which moves so that its distance from (2,3) is always equal to its distance from the line x+2=0
Click here to see answer by stanbon(75887)

Question 1071340: Derive the equation of the locus of a point, the sum of the squares of whose distances from the coordinate axes is 9.
Click here to see answer by ikleyn(52799)

Question 1071338: Please help: A point P(x,y) moves in such a way that its distance from (3,2) is always one half of its distance from (-1,3). Find the equation of its locus.
Click here to see answer by rothauserc(4718)

Question 1071454: an ellipse has an equation of ax^2 +by^2 +f = 0 passing through (4,0) and (0,3)
a. find the equation of the ellipse
b. find the eccentricity of the ellipse
Click here to see answer by ikleyn(52799)

Question 1071450: an ellipse has an equation of Ax^2 + By^2 + f = 0 passing through (4,0) and (0,3)
a. Find the equation of the ellipse
b. Find the Eccentricity of the ellipse
Click here to see answer by ikleyn(52799)

Question 1071489: A system containing a circle and a parbola has 3 solutions. Find the system ( set of equations of the circle and the parbola) using the following information. Show your work.
・The center of the circle is at the origin (0,0)
・The parbola opens upward.
・The vertex of parbola is on the y=axis.
・one of the solutions is (root(7),3).
Click here to see answer by KMST(5328)

Question 1071488: Find the range of k in the of equations below if this system has 2 real solutions. Show your work. y=(x-1)^2+3 & y=2x+k
Click here to see answer by KMST(5328)

Question 1071518: Find the equation of the parabola focus(-5,3) ; directrix y=7
Click here to see answer by josgarithmetic(39620)

Question 1071603: Find the equation of the hyperbola with center at (4,-1) transverse axis parallel to the y axis, distance between foci is 10 and latus rectum is 9/2
Click here to see answer by Edwin McCravy(20059)

Question 1071045: Vertex at x=y axis parallel to 0x / & passing through (6,-3) & (3,4)
Please help me to answer this question I really need th3 answer now. Thanks in advance
Click here to see answer by Fombitz(32388)

Question 1071766:
Click here to see answer by Alan3354(69443)

Question 1071940: How can I find the parabola with two points? for example (-1,3) into y=ax^2

Click here to see answer by Alan3354(69443)

Question 1072086: How can I find the equation of a parabola with vertex at (2,3) and directrix is x=5?
Click here to see answer by josgarithmetic(39620)

Question 1072237: The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 500 feet apart and 60 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 125 feet from the middle of the bridge?
Click here to see answer by stanbon(75887)

Question 1072280: Find the equation of the ellipse with the following properties. Express your answer in standard form.
Vertices at ( 1, 5 ) and ( 7, 5 ) e = 1/3

Click here to see answer by ikleyn(52799)

Question 1072399: What is the equation of parabola if vertex is(1,1)and focus is (1,2) ?
Click here to see answer by Alan3354(69443)

Question 1072508: Hello! How can I find the focus and the directrix of the following equation: (y+2)^2=-12(x-5)
Thank you!
Click here to see answer by rothauserc(4718)

Question 1072507: Hello! I need help with the following question.
Graph the following parabola:
(x-3)^2=8(y+5). I only know how to find the vertex ( 3,5) and p which is 2. But I do not know how to find the focus and the directrix.
Thank you!
Click here to see answer by josgarithmetic(39620)

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