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

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Question 1137550: A skateboarder decides to jump off a ramp. The path of the jump from the ramp can be approximated by: h=-3t^2+6t+1, where h is the height above the ground in metres, s is the horizontal displacement and t is the time after leaving the ramp in seconds. Show that the maximum height reached by the skateboarder is 4m.
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Question 1138673: write an equation of an ellipse in standard form with the center at the origin and the given characteristics.
Vertex at (-5,0) and co-vertex (0,4)
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Question 1138809: equation of a parabola with vertex (2,3) and passing through (1.5,4)
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Question 1138876: Write an equation for the set of all points in the plane equidistant from (-4.-13/2) and x=4.
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Question 1139870: The problem I'm having is how to solve:
Center: (-16,9)
Tangent to y=11
The directions tell me to write the standard form equation of a circle but I kept getting the wrong answers. I feel like I'm getting some steps wrong.
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Question 1140140: Please help me solve this equation

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Question 1140140: Please help me solve this equation

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Question 1140262: Find the equation of the elipse that satisfies these conditions
center (-7,3)
Endpoints of major and minor axes (0,3),(-7,12),(-14,3),(-7,15)
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Question 1140354: Find an equation for the parabola with focus (4,6) and directrix on the x-axis.
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Question 1140354: Find an equation for the parabola with focus (4,6) and directrix on the x-axis.
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Question 1140391: the parabolic dish for a satellite television company is 24 inches across and 12 inches deep. if the signal receiver is located at the focus of the parabola.
how far should it be placed from the base of the dish
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Question 1140704: I have no clue how to start off with this problem. Any help would be great.
Dish antennas have a parabolic cross-section. This concentrates signals onto a sensor at the focus of the parabola. A dish antenna is 1 meter wide and 20 centimeters deep. How far from the bottom of this dish should the sensor be positioned?
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Question 1140779: In advance, thank you for trying to help!
In a room shaped like an ellipse, something whispered at 1 focus can be clearly heard at the other focus. The U.S. Capitol National Statuary Hall in Washington, D.C. is such a whispering gallery. From 1807 to 1857, the U.S. House of Representatives met in this room. According to legend, when John Quincy Adams was a representative following his presidency, he used to look as though he was asleep at his desk during debate, but he was listening to what representatives of the opposing party on the other side of the room were whispering. If the elliptical pattern of this whispering gallery is 92 feet long by 58 feet wide, how far from the whisperer at 1 focus is the listener at the other focus?
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Question 1140688: Find the parametrization for the curve.
The line through the points (5, -2) and (8, 2)
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Question 1140680: Vertex (0, square root 29); Co-vertex (-5,0)
Writing an equation
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Question 1140692: Determine the eccentricity, the type of conic, and the directrix.
r = (9)/(5 +6 cos θ)
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Question 1141094: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. Write the standard form of the equation of the conic and state its name.
x^2 +4y^2 +20x-40y+300=0
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Question 1141334: If we assume that Icarus' orbit lay flat in the same plane as Earth's orbit, approximately how far apart would be the points of intersection of the 2 elliptical orbits? Your result must be accurate to within 0.1 AU. Explain or show how you found this distance.
(Fortunately, Icarus' orbit is tilted with respect to the Earth's orbital plane. Icarus will come relatively close to the Earth in 2015, when Icarus' nearest approach will be about 22 times the distance of the moon from Earth.)
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Question 1141350: Find an equation for the hyperbola with C(2,4), foci F1(2,1) and F2(2,7), and
vertices V1(2,6) and V2(2,2)
Click here to see answer by Edwin McCravy(20056)

Question 1141354: Find the equation for the conic whose graph is shown.
So the graph shows a parabola with the vertex at (-6,0) and directrix at x=-12
Also, the parabola is opening to the right
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Question 1141501: Find and write down equation of the hyperbola that passes through points (3,2)
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Question 1141608: Translate the axes to eliminate the first degree terms of
Thank you.
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Question 1141674: A reflecting telescope's mirror diameter is 76 inches and depth is 42 inches. Where would the focus of the mirror be located? Answer to the nearest hundredth.

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Question 1141738: Find a new representation of after being rotated through an angle of 60 degrees. The question asks for the coefficient of . I get -64, but not sure if that's right. Thank you! Your work is much appreciated!
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Question 1141636: Translate the axes to eliminate the first degree terms of
. Find h and k. Thank you.
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Question 1142040: Is the sequence 2, 4, 8, 16, ... arithmetic? If so, find the common difference.
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Question 1142039: Write the first four terms of the sequence defined by the explicit formula an = n! / n(n + 1).
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Question 1142038: Determine which of the conic sections is represented.
4x² + 14xy + 5y² + 18x − 6y + 30 = 0
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Question 1142038: Determine which of the conic sections is represented.
4x² + 14xy + 5y² + 18x − 6y + 30 = 0
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Question 1142123: please help me understand this and help me answer it
The circle is tangent to line 5x + 12y= 26 and the center is at the origin
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Question 1142123: please help me understand this and help me answer it
The circle is tangent to line 5x + 12y= 26 and the center is at the origin
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Question 1142126: What is the focus, directrix, axis of symmetry, and vertex of 5^2=100y?
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Question 1142331: Look for the center and radius in the given circle equation.
4x²+4y²+40x-32y=5
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Question 1142331: Look for the center and radius in the given circle equation.
4x²+4y²+40x-32y=5
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Question 1142331: Look for the center and radius in the given circle equation.
4x²+4y²+40x-32y=5
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Question 1142359: 4x²-12y²-8y-12y+100=0
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Question 1142490: Classify the conic section and explain how you know.
y2 = x2 - 5x + 6
===========
--> x^2 - y^2 - 5x + 6 = 0
x^2 & y^2 have opposite signs --> hyperbola

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Question 1142826: What is the standard equation of the circle which has (-1,3) and (2,4) as the end points of a diameter
I followed a YouTube tutorial and want to make sure that I am right
So I used the midpoint formula (-1+3)/2,(2+4)/2= (1,3)
Then I used the formula for finding the radius r=1/2squareroot of (2-(-1)^2+(4-3)^2 I evualated it then got squareoot of 5/2
And r^2=(5/2)^2 = 5/4
And I got the standard equation (x-1)^2+(y-3)^2= 5/4

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Question 1142930: Find the value of k such that the graph of the equation k(x^2 + y^2) + x^2 - y^2 + x + y = 0 is a hyperbola.
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Question 1142976: The center of circle of a partical a radius 10 is on the origin. Which of the following points points lies with in the circle
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Question 1142969: A street with two lanes, each 10 ft wide, goes through a semicircular tunnel withradius 12 ft. How high is the tunnel at the edge of each lane? Round off to 2 decimals off to 2 decimals places.
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Question 1142988: The orbit of Earth around the sun is in the shape of an ellipse where the sun is at one of the foci, and whose length of the major axis is 185.8 million miles. If the distance of the sun from the center of the orbit is 1.58 million miles, find the least and greatest distance of Earth from the sun.
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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