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

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

Question 194144: : how would you find the foci of this ellipse?
x^2+9y^2=1
Click here to see answer by stanbon(75887)

Question 194164: x^2+y^2=25
x-2y=-5
Click here to see answer by RAY100(1637)

Question 194162: 1. Find the demensions of a rectangle whose perimeter is 50m and whose area is 144 m2.
Click here to see answer by checkley77(12844)

Question 194321: The product of two numbers is 2, and the sum of their squares is 17/2. Find the numbers.
Click here to see answer by edjones(8007)

Question 194631: Describe the graph of each equation.
y=1/x
how would you describe this? I dont understand the answer in my book.
Click here to see answer by RAY100(1637)

Question 194672: i keep coming up with the wrong answers for the foci of this equation. please help.
4x^2-y^2+1=0
Click here to see answer by RAY100(1637)

Question 194672: i keep coming up with the wrong answers for the foci of this equation. please help.
4x^2-y^2+1=0
Click here to see answer by solver91311(24713)

Question 194702: Can you please help me with this problem?
The directions say to find the real solutions of each system.
WE are using either the elimaniton method or the substitution method

Click here to see answer by solver91311(24713)

Question 194741: Identify the following conic. That is, circle, parabola, hyperbola or ellipse?
x2 - 4y2 - 4x - 24y = 48
Click here to see answer by solver91311(24713)

Question 194756: Is this correct: What is the equation of a parabola with vertex (0,0) and focus (0,4)?

If not where did I go wrong?
Click here to see answer by solver91311(24713)

Question 194756: Is this correct: What is the equation of a parabola with vertex (0,0) and focus (0,4)?

If not where did I go wrong?
Click here to see answer by Edwin McCravy(20059)

Question 194752: The question ask: The graph of y=2x^2+12x+1 is: a parabola whose vertex is ?
Click here to see answer by Alan3354(69443)

Question 194785: i have to write an equation of the line that is tangent to the circle at that point:
x^2+y^2=50; (-7,1)
Click here to see answer by Edwin McCravy(20059)

Question 194785: i have to write an equation of the line that is tangent to the circle at that point:
x^2+y^2=50; (-7,1)
Click here to see answer by josmiceli(19441)

Question 194803: (x+5)2= -(y-9)
Click here to see answer by solver91311(24713)

Question 194808: i have to write the equation of the conic section in standard form and classify the conic section:
9y^2-x^2+2x+54y+62=0
Click here to see answer by solver91311(24713)

Question 194969: Write an equation of a circle with center at the origin and radius 6.
This is what I have.
x2 x y2 = 6squared.
x2 x y2 = 36
Click here to see answer by Alan3354(69443)

Question 194957: Identify the following conic. Is it a circle, parabola,hyperbola or eclipse.
x2 - 4y2 - 4x 24y = 48
Click here to see answer by Alan3354(69443)

Question 195009: Can someone please check to see if I sloved the following problem correctly...
Question
3x + 4y + z = 7
2y + z = 3
-5x + 3y + 8z =-31
My Answer
2 = 3 - 2y
3x + 4y + 3 - 2y = 7
3x + 2y = 4
y= 4 - 3x
------
2
-6 + 4y + 3 - 2y =7
2y = 10
y = 5
10 + z = 3
z = -7
-5x + 6 - 9x + 24 - 16y = -31
----
2
-5x + 6 - 9x +24 - (64-48z) = -31
--- ------
2 2
-5x - 9x + 24z = -31-30+32
---
2
-10x -9x + 48x= -58
29x = -58
x= -2
x=-2 y=5 z= -7
Click here to see answer by Alan3354(69443)

Question 195022: Please let me know if this is correct.
Question: Write an equation of the circle with center (-2,-3) and radius 8.
Answer:
(x+2)2 +(y+3)2=64
x2+4x+4+y2+6y+9=64
x2+y2+4x+6y-51=0
Click here to see answer by RAY100(1637)

Question 195023: Please let me know if this is correct.
Question: Given the equation of a circle is x2+y2-10x+4y+13=0, find its centerand its radius.
Answer:
x2-10x+25+y2+4y+4=-3+25+4
(x-5)2 +(y+2)2=16
Center (5,-2)
Radius 6
Click here to see answer by RAY100(1637)

Question 195037: What is the axis of symmetry of the parabola with the equation x-4=(1/4)(y+1)^2?
Click here to see answer by RAY100(1637)

Question 195161: Can you please help me with this.
The directions say For each system graph the equations, determine the number of solutions, and estimate each real solution to the nearest half-unit.

Click here to see answer by solver91311(24713)

Question 195166: Can you please help me with this.
The directions say solve each system algebraically.

Click here to see answer by anantha(86)

Question 195131: hyperbola
(x+2)^2
________
25
(x+2)^2
________
25
minus
(x+2)^2
________
25
equals
1
find the center, foci, vertices, length of the transverse and conjugate axis, and the asymtopes

Click here to see answer by Edwin McCravy(20059)

Question 195312: please help. I cannot graph the second equation for some reason. is it a parabola? please explain this to me.
By sketching graphs, find the number or real solutions the system has.
x^2 -4y^2=4
6y^2-x=2
Click here to see answer by Alan3354(69443)

Question 195408: Find the equation for a parbola with the vertex (-2,3), and focus (-5,3).
Click here to see answer by mersha(9)

Question 195478: explain how you can tell whether a parabola opens upward, downward, to the left, or to the right
Click here to see answer by stanbon(75887)

Question 195669: I have a "conic invasion" worksheet. I have to tell by the equation the type of figure and the specific info needed to graph the equation. PLEASE HELP ME! im not asking for the answers or anything (unless youre feeling generous :) just how to get these started im totally lost.
1.y^2+9(x+13)^2=9
2.x^2+y^2=144 for 10>or=y>or=-12
3.x^2+y^2+10x-10y+46=0
4.y+1=0 for 2>or=x>or=-2
5.2x^2-49y+392=0 for y 6.(y^2)/9 + [(x-13)^2]/1=1
7.3x+2y=4 for 2>or=x>or=0
8.2x^2-49y=294 for y 9.15x+7y=175 for 7>or=x>or=-2
10.5x^2-49y=441 for y 11.15x-7y+175=0 for 0>or=x>or=-2
12.3x-2y+4=0 for 0>or=x>or=-2
13.(x-5)^2+(y-5)^2=4
Click here to see answer by jim_thompson5910(35256)

Question 195695: I need to convert this equation to standard form:
16x^2 + 4y^2 + 96x - 8y + 84 = 0
I know the standard form is x^2/a^2 + y^2/b^2 = 1
How do I begin?
Click here to see answer by Alan3354(69443)

Question 195772: Please help me put this in standard form x^2 - 4x + y^2 + 8y - 16 = 0
Click here to see answer by stanbon(75887)

Question 195593: a Find the x intercepts for the parabola y = x2 � 6x + 5.
b Find the vertex of the parabola y = - 2x2 + 8x + 4

Click here to see answer by jojo14344(1513)

Question 195830: Find the center and radius of a circle whose diameter has these endpoint (22,23) (14,8)
Click here to see answer by solver91311(24713)

Question 196069: I need help with a problem.
the directions are find all points of intersection. It is a problem our teacher made up but the problem is for our section for solving quadratic systems
equation 1-x^2+y^2+4x-6y+4=0
equation 2-x^2+y^2-4x-6y+12=0
Click here to see answer by vleith(2983)

Question 196080: Use the following hyperbola to answer all questions.
Find the center, foci, vertices, the length of the transverse and conjugate axis and the asymtotes for the following hyperbola.

Click here to see answer by Edwin McCravy(20059)

Question 196133: how do you write the standard form of the equation of the conic section?
Click here to see answer by Alan3354(69443)

Question 196188: what is the general equation of the ellipse which has a foci at (-4,2) and (4,2) and passing through (1,3)
Click here to see answer by stanbon(75887)

Question 196187: what is the general equation of the parabola which has a foci at (-4,2) and (4,2) and passing through (1,3)
Click here to see answer by stanbon(75887)

Question 196282: Identify the conic section represented by each equation. For a parabola, give
the vertex. For a circle, give the center and radius. For an ellipse or a
hyperbola, give the center and foci. Sketch the graph.
35. x2 - 4y2 + 4x + 8y - 16 = 0
36. 25x2 + 4y2 - 50x - 24y - 39 = 0
37. x2 + y2 - 4x + 2y + 1 = 0
38. x2 - 4x - y + 7 = 0
39. x + 2y2 + 4y - 2 = 0
40. x2 + 9y2 + 8x - 54y + 88 = 0
Click here to see answer by solver91311(24713)

Question 196201: Find the radius and center of each circle.

12. (x - 2)^2 + (y - 3)^2 = 16
13. x^2 + (y + 4)^2 = 8
14. (x + 1)^2 + (y - 2)^2 = 12
15. (x - 6)^2 + y^2 = 25
Click here to see answer by anantha(86)

Question 196562: May you please help me with the following hyperbola in standard form:

find the center, foci, the length of one of the two axes (transverse or conjugate) which is parallel to the y-axis, and the two asymptotes

Click here to see answer by Edwin McCravy(20059)

Question 196648: Please help me with making 1/2y^2-3y+13/2 into standard form
Click here to see answer by jim_thompson5910(35256)

Question 196700: Identify the conic section represented by each equation. For a parabola give the vertex. For a circle give the center and radius. For an ellipse or a hyperbola give the center and foci.
(1) x^2+y^2-4x+2y+1=0
I found that the equation would be (x-2)^2 + (y+1)^2=4
This would be a circle
The center would be (2, -1)
The raidus would be 2
(2)x^2-4x-y+7=0
I found that the equation would be y=(x-2)^2 + 7
This is a parabola
The vertex is at (7,2)
Is this correct?
I'm not quite sure if I am doing these right...
Thank you!
Click here to see answer by stanbon(75887)

Question 196696: Identify the conic section represented by each equation. For a poraola, give the vertex. For a circle, give the center and radius. For an ellipse or hyperbola, give the center and foci.
(1) x^2-4y^2+4x+8y-16=0
For this one I found that the equation would be (x+2)^2/16-(y-1)^2/4=1
I got that this is a hyperbola.
I found the center to be (-2,1)
I found the foci to be (4.47,0) (-4.47,0).

(2) 25x^2+4y^2-50x-24y-39=0
For this one I found that the equation would be (x-1)^2/4 + (y-3)^2/25=1
I got that this is an ellipse
I found that the center is (1,3)
I found that the foci is (0,4.58) (0,-4.58)
Is this correct?
I'm not really sure what I'm doing....
Thank you!!
Click here to see answer by Alan3354(69443)

Question 196705: I cannot seem to find the correct standard equation, foci, and asymptotes of the following hyperbola:

I need to write it in this kind of form:

I have been solving these kinds of problems wrong lately, and I am quite worried since it will be a subject on an upcoming test. Any help would be appreciated, and many thanks in advance.
Click here to see answer by Edwin McCravy(20059)

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