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

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Question 1142993: Given point A(0,2) on the parabola y^2=x+4. Points B & C also lie on the curve such that BC is perpendicular to AB. Give the range of point C on the y-axis.
Thanks!
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Question 1144745: A semielliptical archway is to be formed over the entrance to an estate.bthe arch is to be set on pillars that are 10 feet apart and is to have a height (atop the pillars) of 4 feet. Where should the foci be placed in order to sketch the arch?
Click here to see answer by KMST(5410)

Question 1146372: Find the equation of the radical axis of the two circles x2 + y2 - 4x - 6y - 3 = 0 and x2 + y2 - 12x - 14y + 65 = 0.
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Question 1147397: find the canonical form and determine the nature of conics
8x^2-12xy+17y^2+16x-12y+3=0
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Question 1150043: Write an equation for the hyperbola that has eccentricity 2, center at (0,0), and vertex at (0,8)
An equation for the hyperbola is...?
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Question 1152643: Find the value/s of U so that the graph of the equation of Ux2 + y^2 − 2Ux = 0 is a hyperbola.
Afterwards, identify the distance/s between the foci.
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Question 1158804: 9x^2-24xy+16y^2-20x-15y-50=0
Use axis rotation formulas for x and y to transform the quadratic equation to an equation in (u,v) coordinates with no cross product term. Identify the vertex or vertices in (x,y) coordinates
thank you so so so much
Click here to see answer by KMST(5410)

Question 976252: a one-way road passes under an overpass in the shape of half and ellipse, 30ft high at the center and 20ft wide. Assuming a truck is 12ft wide, what is the tallest truck that can pass under the overpass?
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Question 46730: The graph of xsquare unit +y square unit =9 is translated 4 units to hte right and 5 units up. Find the equation of the new circle.
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Question 41391: y=2sin(1/4)x
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Question 47802: find all real solutions: 2squaredx-24(2squared)=256
i know this doesnt make much sense. i had to put squared in as words because i cant get the symobol you know the small 2
thanks for all fo your help
Click here to see answer by ikleyn(53965)

Question 1164281: A flashlight is shaped like a paraboloid, so that if its light bulb is placed at the focus, the light rays from the bulb will then bounce off the surface in a focused direction that is parallel to the axis. If the paraboloid has a depth of 1.8 in and the diameter on its surface is 6 in, how far should the light source be placed from the vertex? (Round off your answer to 2 decimal places and don't include the unit)

Click here to see answer by KMST(5410)

Question 1164605: A flashlight shaped like paraboloid, so that if the bulb is focused, the light rays from the bulb is faced at the focus, the light rays from the bulb will then bounce off the surface in a focused direction that is parallel to the axis. If the paraboloid has a depth of 1.8 and the diameter is 6 in, how far should the light source be placed from the vertex?

Click here to see answer by greenestamps(13372)

Question 1164537: 1)Find a new representation of the given equation after rotating through the given angle.
11x^2-50√3xy-39y^2+576=0 60degrees
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Question 443624: Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2 Please show all of your work.
Click here to see answer by ikleyn(53965)

Question 729528: what is the center, verticies, foci and eccentricity of 3x^2 +2y+18x-2y-8=0
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Question 1165107: Find the equation of the parabola given vertex at (4, 3), axis of symmetry 𝑦 = 3, length of the latus rectum is 4, and 4𝑝 > 0
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Question 1165709: arch in an amusement park has a parabolic shape. it has a height of 74 feet and the base width of 38 feet. what is the height of the Arch 8 feet from the center?
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Question 1165937: solve for the equation of the hyperbola in general form with directrices x=-5 and x=7, and one focus at (13,5).
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Question 740852: What is the center and radius of the circle x^2+y^2-8x-10y+32=0 ?
Click here to see answer by ikleyn(53965)

Question 748181: Write an equation of an ellipse with the given characteristics.
Center (0,0), vertical major axis of length 12, minor axis of length 4
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Question 619259: Find the center and radius of a sphere, x^2+y^2+z^2-4x+2y-6z+10=0
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Question 552371: What is the axis of symmetry of y=7(x+1)(x-3) I have tried another website and it stated something about h=x, and h would be the 1 in the first set of parenthesis, correct? Or is there some other method that is more accurate? Thank you.
Click here to see answer by ikleyn(53965)

Question 1168977: Conjugate axis along the y-axis, ome vertex at (0,7), asymptotes are 6x-5y+30=0 and 6x+5y-30=0. Need help finding the Equation of this hyperbola. How?

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Question 1209794: (x+4)^2/9+(y+3)^2 /4 =1

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Question 1167285: A router is in the library of the university which is 1.5 years away from a student lounge. The range of the router, which services the WIFI connection of the university, has a diameter of 3.5 meters, with it as the center. Can students staying in the lounge connect to the said WIFI?
Click here to see answer by ikleyn(53965)

Question 1167416: The tower stands 180 meters tall. The diameter of the top is 75 meters. At their closest, the sides of the tower are 60 meters apart. Find the equation of the hyperbola that models the sides of the cooling tower. Assume that the center of the hyperbola is the origin. Round of final answer to the nearest whole number.
Click here to see answer by ikleyn(53965)

Question 1167713: 1. Kepler observed that Pluto orbits the sun in an elliptic motion. With the
sun at one focus, nearest that Pluto gets to the Sun is 4,400,000,000 km, and the farthest that it goes to the Sun is 7,400,000,000 km.
a) Assuming that the center of Pluto’s orbit is at (0, 0), find the equation
that models Pluto’s orbit.
b) If an unidentified planet is located in the other focus, how far is this
planet from the Sun?
Click here to see answer by ikleyn(53965)

Question 1168412: The Bayonne bridge connects Staten Island, New York to New Jersey. It has an arch in the shape of parabola that opens downward. Write an equation of the parabola to model the arch, assuming that the origin is at the surface of the water. 325. ft and 1675ft
Click here to see answer by CPhill(2264)

Question 1165099: A cable hangs in the form of a branch of a hyperbola between two poles that are 20 meters apart. The poles
are 70 meters high and the cable has a sag of 2 meters midway between the poles. Find the height of the cable
at a point 3 meters from one of the poles.
PLEASE HELP ME HUHUHU. THANK YOU SO MUCH!!
Click here to see answer by ikleyn(53965)

Question 1168931: Find the (standard) equation of the hyperbola whose foci are 𝐹1(-3,0) and 𝐹2(3,0),
such that for any point on it, the absolute value of the difference of its distances
from the foci is 3.
Click here to see answer by ikleyn(53965)

Question 1168800: Write an equation in standard form of the parabola that has the same shape as the graph of
f(x)= 4x^2 or
g(x)=−4x2, but with the given maximum or minimum.
Maximum=7 at x=-2

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Question 1168877: Find the length of latus rectum (LR) is 10, vertex at the origin; parabola opens to the right.
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Question 1168920: Find the equation of the ellipse if the endpoints of minor axis are (1,3) and (1,-1) with a focus at (-1,1).Express your answer in general form.

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Question 1168978: Foci at (-1,4) and (7,4), transverse axis has the length 8/3. Whats the equation
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Question 1169000: find the equation of the ellipse if the vertex is at (5,1) and foci at (-2,1) and (4,1). express your answer in general form.
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Question 1169047: At this point, you are now ready to take the summative assessment for learning plan 3. Place your answers on a whole sheet of paper. Show your complete solution. (20 points)
1. Write the standard form of the equation of the hyperbola with the following characteristics:
Center at (2,3)
Vertices at (-1,3) and (5,3)
Covertices at (2,-2) and (2,8)
Click here to see answer by MathLover1(20855)

Question 1169036: find the equation of the ellipse if the endpoints of minor axis are (1,3) and (1,-1) with a focus at (-1,1).
Click here to see answer by mccravyedwin(421)

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