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

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Question 36142: How do mathematicians get the formula: lal = 1/4c (absolute value of 'a' equals one-fourth times 'c')? This formula is used to determine the equation of a parabola. Please explain how mathematicians got this formula. Thank you for your time.
Julia
Click here to see answer by venugopalramana(3286)

Question 36551: I was wondering if anyone could help me determine what type of figure is given, then graph. Show all work and label all key points (asymptotes, foci, vertices, the directrix, the center) where applicable.
4(x-1)2 = 4-y^2
Click here to see answer by venugopalramana(3286)

Question 36550: I was wondering if anyone could help me determine what type of figure is given, then graph. Show all work and label all key points (asymptotes, foci, vertices, the directrix, the center) where applicable.
9x^2 � 96y = 16y^2 + 18x + 279
Click here to see answer by venugopalramana(3286)

Question 36549: I was wondering if anyone could help me determine what type of figure is given, then graph. Show all work and label all key points (asymptotes, foci, vertices, the directrix, the center) where applicable.
x^2 � 4x � 8y = 12
Click here to see answer by venugopalramana(3286)

Question 36547: Determine what type of figure is given, then graph. Show all work and label all key points (asymptotes, foci, vertices, the directrix, the center) where applicable.
X^2 + y^2 + 4x � 6y = 3
Click here to see answer by venugopalramana(3286)

Question 36546: Determine what type of figure is given, then graph. Show all work and label all key points (asymptotes, foci, vertices, the directrix, the center) where applicable.
X2 + y2 + 4x � 6y = 3
Click here to see answer by venugopalramana(3286)

Question 36677: find the verical and horizontal asymptotes of the following functions:
1) f(x)=(2x^2+5x^2-3)/(x^2+2)
2) f(x)=1/(x-3)^2
thank you
Click here to see answer by stanbon(75887)

Question 36676: find the domain of the following functions by determining which numbers, if any, cannot be used:
1) f(x)=3x^2/(1+3x)
2) f(x)=(x^2+x-2)(x^2+4)
Thank you.
Click here to see answer by stanbon(75887)

Question 36700: write the equation of the given circles in standard form:
1) x^2+y^2-6x+8y+9=0
2) 2x^2+2y^2-4x-28y+66=0
Click here to see answer by venugopalramana(3286)

Question 36699: write the equation of the specified parabola:
1) vertex (0,0) and focus (0,3)
2) vertex (2,0) and focus (0,0)
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Question 36698: partial fraction decomposition; use the partical fraction decomposition to "decompose" the following functions:
1) (x-8)/(x^2-3x-28)
2) (-x)/(x^2+3x+2)
Click here to see answer by venugopalramana(3286)

Question 36675: Write the equation of the specified ellipses:
1) Vertices = (7,0) and (-7,0) and Foci = (6,0) and (-6,0)
2) Foci = (3,0) and (-3,0) and major arc is length of 12
Thank you.
Click here to see answer by venugopalramana(3286)

Question 35524: sketch and find the equation
Foci=(2,6) and (2,-6)
difference in focal radii is 4
that is all the information that it gives me. and i have to sketch and find the equation using that information
Click here to see answer by venugopalramana(3286)

Question 36905: (x+3)squared=8(y+2)
Is this ellipse, parabola or hyperbola
Click here to see answer by Alwayscheerful(414)

Question 36903: (x+3)squared=8(y+2)
Is this ellipse, parabola or hyperbola
Click here to see answer by venugopalramana(3286)

Question 37527:
Alphonse strats strats at point A and runs at a constant rate toward point C. At the same time, Brigitte strats at point B and runs toward point C also at a constant rate.They arrive at C at exactly the same moment. I f they continue running in the same directions, Alphonse arrives at B exactly 10 seconds before Brigitte arrives at A. How fast was Brigitte running? 60m 40m ____________________________________________ A C B

Click here to see answer by AnlytcPhil(1806)

Question 37841: what is the vertex and axis of symetry of parabola with equation y=2x^2 +8x+3.
I tried to complete the square and i got the vertex to be (-2,-1) but the answer sheet the teacher gave says the vertex is (-2,-5)? What did I do wrong?
Click here to see answer by stanbon(75887)

Question 37812: Please help me with the following:
A unit circle is centered at the origin undergoes transformations.
(x-3)^2 + (y+4)^2 = 25 is the resulting equation, describe the transformations the unit circle underwent.
Click here to see answer by fractalier(6550)

Question 37900: Hello. I need help with the following problem:
Write the equation of the parabola: y=4x^2-8x+1
Thank you.
Click here to see answer by Alwayscheerful(414)

Question 37947: Two microphones that are placed 2000 feet apart record an explosion. The first microphone receives the sound one second before the second. Where did the explosion come from?
Click here to see answer by fractalier(6550)

Question 38069: 1.A pendulum swings through an arc of 660 centimeters. On each successive swing, the length of the arc is 6/7 of the previous length. Find th total distance the pendulum travels before it comes to rest.
Click here to see answer by fractalier(6550)

Question 34188: Express as a single logarithm and simplify:
logx+logy-logz-logw
how do I do this one?
Click here to see answer by fractalier(6550)

Question 38073: 1.A pendulum swings through an arc of 660 centimeters. On each successive swing, the length of the arc is 6/7 of the previous length. Find th total distance the pendulum travels before it comes to rest
Click here to see answer by fractalier(6550)

Question 38194: m^2 + 3n^2 = 11
m - n = 2
Conic - systems of two non-linear equations (two solutions)

second question: y = x^2 and 7x = y + 12 (one solotion from these equations)
Click here to see answer by fractalier(6550)

Question 38222: standard form of parabola vertex (0,0) and focus (0,5)
and
equation of ellipse vertex (-8,0), co-vertex (0,4) center (0,0)

Click here to see answer by Nate(3500)

Question 38295: name the vertex for the parabola with equation y=3x�-12x+16
Click here to see answer by Nate(3500)

Question 38295: name the vertex for the parabola with equation y=3x�-12x+16
Click here to see answer by Paul(988)

Question 38304: Find the slopes of the assymptotes of the hyperbola with equation x�/64 - y�/36=1
Click here to see answer by Nate(3500)

Question 38316: Classify the following as parabolas, ellipses, hyperbolas or circles.
x�+y�-10x+9=0
4y�+9=x
6x�+10y�=60
Click here to see answer by Nate(3500)

Question 38329: what is the foci of the ellipse with the equation x�/16+y�/25=1
Click here to see answer by Nate(3500)

Question 38323: find the foci of the hyperbola with equation y�/144-x�/100=1
Click here to see answer by Nate(3500)

Question 38331: what is the foci of the hyperbola with the equation y�/144-x�/100=1
Click here to see answer by Nate(3500)

Question 38322: find the foci of the ellipse with equation x�/16+y�/25=1
Click here to see answer by Nate(3500)

Question 38335: find the equation for the parabola with focus (1,4) and directrix x=-3
Click here to see answer by Nate(3500)

Question 38337: What are the foci of the ellipse with equation (x^2/100)+(y^2/64)=1
a.(0,+or- sqroot of 164)
b.(+or- sqroot of 164,0)
c.(0,+or- 6)
b.(+or- 6,0)
i got b in part guess mode ^_^
Click here to see answer by Nate(3500)

Question 38377: 1) Find the vertices and foci of the ellipse
4x2 + 25y2 - 16x + 100y = -16
2) Find the center and asymptotes of the hyperbola
4x2 - 9y2 - 8x - 18y = 41
3) solve the system x2 + y2 = 16 and x2/16 + y2/9 = 1
4) find the center and radius of the circle
x2 + y2 -4x + 2y = 4
Click here to see answer by Nate(3500)

Question 38195: if vertex of a parabola is (2,1) and focus is (1,-1) so what is the eqation of this parabola.
Click here to see answer by fractalier(6550)

Question 38517: Compare the area of a circle with a radius of 10 units and the area of an ellipse with a major axis of 10 and a minor axis of 6. Show what equations you use to find the area od each figure and then compare each.
Click here to see answer by Nate(3500)

Question 38557: The question is write an equation for the perpendicular bisector of the line segment joining the two points?
the points are (0,0)(-8,-10)
how would you solve this
Click here to see answer by venugopalramana(3286)

Question 38654: ellipse problem #11 find vertices, foci
2x^2+y^2=3
I can't figure out how to put in (x^2/a^2)+(y^2/b^2)=1 form. How do I get rid of the 2 from 2x? and make 3 into 1?
Click here to see answer by Nate(3500)

Question 38739: When looking at an equation of a hyperbola in general form, how do you tell the difference between a hyperbola that opens up and down (y^2-x^2=1) and a hyperbola that opens left and right (x^2-y^2=1) without writing the equation in standard form? I know AC<0
Click here to see answer by Nate(3500)

Question 38782: Find the equation of the ellipse whose center is (5,-3)that has a vertex at (13,-3) and a minor axis of length 10.
Click here to see answer by Nate(3500)

Question 38780: Find the center, vertices, and foci for the ellipse: 4x^2+16y^2=64
Thanks:)
Click here to see answer by Nate(3500)

Question 38778: Please....Find the vertex,focus, and directix of the graph of the equation
8(y+2)=(x+6)^2
Click here to see answer by Nate(3500)

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