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

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

Question 1181167: Dearest Sir,
Please, I need your help about this problem. Help me solve it and also please show your solution.
Convert the general equation 9𝑥2 + 16𝑦2 − 54𝑥 − 64𝑦 + 1 = 0 to standard form. Sketch and determine the parts of an ellipse.
Solve the value of a, b, and c.
Parts of an Ellipse
1. Center
2. Foci
𝐹1
𝐹2
3. Vertices
𝑉1
𝑉2
4. Co-vertices
𝐵1
𝐵2
5. Endpoints of Latus Rectum
𝐸1
𝐸2
𝐸3
𝐸4
6. Directrices

7. Eccentricity
8. Length of LR
9. Length of Major Axis
10.Length of Minor Axis
Thank a lot and God bless you.
Sincerely yours,
Lorna
Click here to see answer by MathLover1(20850)

Question 1181166: Dear Sir,
Please help me solve this problem and please show me your solution.
Given by the equation 49𝑥2 + 9𝑦2 = 441, sketch and determine the parts of an ellipse.
Solve for the value a, b, c
Parts of an Ellipse
1. Center
2. Foci
𝐹1
𝐹2
3. Vertices
𝑉1
𝑉2
4. Co-vertices
𝐵1
𝐵2
5. Endpoints of Latus Rectum
𝐸1
𝐸2
𝐸3
𝐸4
6. Directrices
7. Eccentricity
8. Length of LR
9. Length of Major Axis
10.Length of Minor Axis
Thank you very much. More Power.
Sincerely yours,
Lorna
Click here to see answer by MathLover1(20850)

Question 1181164: Dear Sir,
Please help me solve this problem and kindly show me your solution.
Find the general equation of the of the parabola with vertex at (5, −3) and focus at (6, −3).
Sketch and determine the parts of the parabola.
Solve the value for C
Parts of the Parabola
Parts of the Parabola
1. Vertex
2. Focus
3. Directrix
4. Axis of Symmetry
5. 𝑬𝟏
𝑬𝟐
6. Length of 𝐸1, 𝐸2
7. Graph
Thank you very much.
And more power.
Sincerely yours,
Lorna
Click here to see answer by MathLover1(20850)

Question 1181181: Dear Sir
Please help me solve this problem.

Find the general equation of the of the parabola with vertex at (5, −3) and focus at (6, −3).
Sketch and determine the parts of the parabola.
Parts of the Parabola
1. Vertex
2. Focus
3. Directrix
4. Axis of Symmetry
5. 𝑬𝟏
𝑬𝟐
6. Length of 𝐸1, 𝐸2
Thank you and God bless you.
Lorna
Click here to see answer by Edwin McCravy(20056)

Question 1181515: What type of conic section is this 6x²+9y²-24x-54y+105=0
Click here to see answer by Solver92311(821)

Question 1181515: What type of conic section is this 6x²+9y²-24x-54y+105=0
Click here to see answer by ikleyn(52795)

Question 1182286: Find the x-intercept of the parabola with vertex (4,75) and y-intercept (0,27) write your answer in this form:(x1,y1),(x2,y2)

Click here to see answer by MathLover1(20850)

Question 1182707: when the load is uniformly distributed horizontally, a suspension bridge cable hangs in a parabolic arc. if the bridge is 200 ft long, the towers 40 ft high and the cable 15 ft above the floor of the bridge at the midpoint. find the equation of the cable using the midpoint origin.
Click here to see answer by greenestamps(13200)

Question 1182822: Find the volume of the solid of revolution formed by rotating the region bounded by the parabola y = x2 and the lines y = 0 and x = 2 about the x-axis
Click here to see answer by ikleyn(52795)

Question 1182836: Suppose that the orbit of a planet is in the shape of an ellipse with a major axis whose length is 500 million km.
If the distance between the foci is 400 million km, what is the equation of the orbit?
Click here to see answer by ikleyn(52795)

Question 1182891: Anatomy of a Parabola in Action
The height of a diver above water during a dive can be modeled by
h(t) = -16t^2 + 8t + 20.
where his height in feet and t is time in seconds.
5. Find the line of symmetry.
6. State the meaning of the line of symmetry in terms of the situation.
7. Find the vertex.
8. State the meaning of the vertex in terms of the situation.
9. What is the practical domain?
10. What is the practical range?
Click here to see answer by MathLover1(20850)

Question 1183153: Let y = load in pounds and x = length in feet. In two or more complete sentences, describe the relationship between the variables x and y in terms of length and weight.
Click here to see answer by josgarithmetic(39618)

Question 1183272: Think about the standard parabola defined by y=x^2. How does the parabola
defined by y=-4(x+3)^2-7 compare to the standard parabola? Describe all of
the transformations. Then, draw a reasonable sketch of both parabolas. Appreciate the help
Click here to see answer by Solver92311(821)

Question 1183327: A circle is tangent to the line 3x-4y -4 = 0 at the point (-4,-4) and the center is on the line
x+y+7 = 0. Find the equation of the circle

Click here to see answer by robertb(5830)

Question 1183440: f(x) = c (x - 3)(x + 3)
In the quadratic equation above, c is a nonzero constant. The graph of the equation in the xy- plane is a parabola with a vertex (h,k), where k = -18. What is c?
Click here to see answer by Boreal(15235)

Question 1183542: The vertices of the ellipse given by 4x² + 25y² = 100 are:
Click here to see answer by MathLover1(20850)

Question 1183543: Find the equation of a hyperbola in the form y²/M - x²/N = 1, M, N> 0 if the center is at the origin, the length of the conjugate axis is 10, and the foci are sqrt(29) units from the center.
Click here to see answer by MathLover1(20850)

Question 1183603: Diameter with endpoints (-2,-1) and (6,3)
Click here to see answer by Solver92311(821)

Question 1183603: Diameter with endpoints (-2,-1) and (6,3)
Click here to see answer by josgarithmetic(39618)

Question 1183604: Center (-2,1)
Click here to see answer by Solver92311(821)

Question 1183604: Center (-2,1)
Click here to see answer by ikleyn(52795)

Question 1183605: Center (-4,9)
Click here to see answer by Solver92311(821)

Question 1183605: Center (-4,9)
Click here to see answer by ikleyn(52795)

Question 1183606: X-intercepts

Click here to see answer by Solver92311(821)

Question 1183606: X-intercepts

Click here to see answer by ikleyn(52795)

Question 1183608: The ceiling of a whispering gallery is in semi-elliptical in shape. Two people at the foci can hear each other whisper, since sound from any focus bounces off the ceiling to the other focus. If the gallery is 46 ft across and 15 ft high at the center, how far apart are the two points where two people should stand so they can hear each other whisper?
Click here to see answer by ikleyn(52795)

Question 1183607: Locate the center, vertices, the foci, and the ends of the latera recta then graph the ellipse whose equation is 4x²+9y²-16x+18y-11=0.
Click here to see answer by KMST(5328)

Question 1183631: a single lane 12ft wide goes through a semicircular tunnel with radius 9ft. how high is the tunnel at the edge of each lane? (round off to 2 decimal places)
Click here to see answer by Boreal(15235)

Question 1183748: Find the orthogonal trajectories of all straight lines
Click here to see answer by ikleyn(52795)

Question 1183750: Find the orthogonal trajectories of the straight lines
Click here to see answer by ikleyn(52795)

Question 1183749: Find all the orthogonal trajectories of all parabolas
Click here to see answer by ikleyn(52795)

Question 1183746: Prove that family of curves x^2/c^2 + y^2/(c^2 -1) is self orthogonal?
Click here to see answer by ikleyn(52795)

Question 1183747: Find the member of orthogonal trajectories which passes through (1, 2) for the family x^2 + 3y^2 = cy?
Click here to see answer by robertb(5830)

Question 1183792: Locate the vertex, the focus, and the ends of the latus rectum and find the equation of the directrix, then draw the parabola whose equation is (y-1)² = -8(x-2).
Click here to see answer by MathLover1(20850)

Question 1183793: The towers of a suspension bridge are 800 m apart and are 180 m high. The cable between the towers hangs in the shape of parabola, which at its lowest just touches the road. How high above the road is the cable 300 m away from the center?
Click here to see answer by ikleyn(52795)

Question 1183810: Equation of parabola y= -x²-3
Click here to see answer by MathLover1(20850)

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