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

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Question 1174416: A 10-feet tall, 10-feet wide truck is approaching a tunnel on a one-way road. The arch at the tunnel’s
entrance forms the upper half of an ellipse with a height of 15 feet at the center and a base of 12 feet wide.
Consider that the center is at the origin, will the truck be able to fit through the arch?
Click here to see answer by CPhill(1959)

Question 1172679: The following application was developed during World War II. It shows how the properties of hyperbolas can be used in radar and other detection systems.
Two microphones, 1 mile apart, record an explosion. Microphone A receives the sound 2 seconds before microphone B. Where did the explosion occur? (assume sound travels at 1100 feet per second.
Click here to see answer by CPhill(1959)

Question 1171519: An arch of a bridge over a highway is semi-elliptical in shape and 50 feet across. The highest point of the arch is 15 feet above the highway. What is the maximum height of a vehicle 10 feet wide that can fit under arch ?

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Question 1170862: An endpoint of the minor axis is at (-1, -10), a vertex is at (-14, 2) and a focus is at (4, 2)

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Question 1171137: Navigational transmitters Q and R are located at (-130,0) and (130,0) respectively. A receiver A on a fishing boat somewhere in the first quadrant listens to pair (Q,R) of the transmissions and computes the difference of the distance from boat Q and R as 240 miles. What is the equation of the hyperbola on which A is located?
Click here to see answer by CPhill(1959)

Question 1209900: Let $x$ and $y$ be real numbers such that
x^2 + 3xy + 2y^2 = 1 - 12x + 5y.
Find all possible values of x + y. Enter your answer using interval notation.

Click here to see answer by CPhill(1959)

Question 1170844: I have a parabola with a length of 72 feet and a height of 64 ft, the goal is to find the vertex as well as the x-intercepts and then write the parabola in standard, vertex and factored form; thanks a ton!
Click here to see answer by CPhill(1959)

Question 1170507: For an object in an elliptical orbit around the moon, the points in the orbit that are closest to and farthest from the center of the moon are called perilune and apolune, respectively. These are the vertices of the orbit. The center of the moon is at one focus of the orbit. A spacecraft was placed in a lunar orbit with perilune at a = 89 mi and apolune at b = 258 mi above the surface of the moon. Assuming that the moon is a sphere of radius 1075 mi, find an equation for the orbit of this spacecraft. (Place the coordinate axes so that the origin is at the center of the orbit and the foci are located on the x-axis. Round each answer to the nearest whole number.)
x2 + y2 = 1

Click here to see answer by ikleyn(52798)

Question 1170541: Two stations, located at M(−1.5,0) and N(1.5,0)(units are in km), simultaneously send sound signals to a ship, with the signal traveling at the speed of 0.33 km/s. If the signal from N was received by the ship four seconds before the signal it received from M, find the equation of the curve containing the possible location of the ship.
Click here to see answer by CPhill(1959)

Question 1170539: A satellite dish is shaped like a paraboloid, with the receiver placed at the focus. It is to have a depth of 0.44 m at the vertex, with the receiver placed 0.11 m away from the vertex. What should the diameter of the satellite dish be?
Click here to see answer by CPhill(1959)

Question 1170538: A satellite dish is shaped like a paraboloid, with the receiver placed at the focus. It is to have a depth of 0.44 m at the vertex, with the receiver placed 0.11 m away from the vertex. What should the diameter of
the satellite dish be?
Click here to see answer by CPhill(1959)

Question 1170527: LORAN navigational transmitters A and B are located at (-130,0) and (130,0) respectively. A receiver P on a fishing boat somewhere in the first quadrant listens to the pair (A,B) of the transmissions and computes the difference of the distance from boat A and B as 240 miles. Find the equation of the hyperbola on P is located.
Click here to see answer by CPhill(1959)

Question 1170522: The cable of suspension bridge hangs in the shape of a parabola. The towers supporting the cable are 400ft apart and 150ft high. If the cable, at its lowest, is 30ft above the bridge at its midpoint, how high is the cable 50ft away (horizontally) from either tower?
Click here to see answer by CPhill(1959)

Question 1206901: The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tower is 288 feet. The smallest diameter of the tower is 143 feet which is 393.5 feet above the ground. The tower is 581 feet tall.
Find the width of the tower at a height of 38 feet.
Click here to see answer by ikleyn(52798)

Question 1170336: Find the focus, directrix, and equation of the parabola with vertex at the origin, axis along y-axis; opening upward; and the length of the latus rectum is 12. Sketch the graph.
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Question 1170335: Find the length of the latus rectum and the equation of the parabola with vertex at the origin, directrix x=-3 and focus (3, 0). Sketch the graph.
Click here to see answer by CPhill(1959)

Question 1169034: A satellite dish has a shape called paraboloid so that its cross-sections through its center (lowest point) are parabolas, all having the same focus. Radio signals sent to it bounce off the surface and are reflected to the focus. The receiver is then placed at the focus. If the satellite dish is 3 meters across and 0.625 meters deep at its center, how far should the receiver be from the center. solution please

Click here to see answer by ikleyn(52798)

Question 1169035: A satellite dish has a shape called paraboloid so that its cross-sections through its center (lowest point) are parabolas, all having the same focus. Radio signals sent to it bounce off the surface and are reflected to the focus. The receiver is then placed at the focus. If the satellite dish is 3 meters across and 0.625 meters deep at its center, how far should the receiver be from the center. solution please

Click here to see answer by ikleyn(52798)

Question 1169787: Two long-range navigation stations A and B lie on a line running east and west,
and A is 88 miles due east of B. An airplane is travelling east on a straight line course
that is 66 miles north of the line tough A and B. Signals are sent at the same time
from A and B, and the signal from A reaches the plane 350 microseconds before
the one from B. If the signals travel at the rate of 0.2 mile/microsecond, locate the
position of the plane.
Click here to see answer by CPhill(1959)

Question 1165555: 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.
Click here to see answer by ikleyn(52798)

Question 1165710: 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.

Click here to see answer by ikleyn(52798)

Question 1167899: Please answer this question, I tried but I don't understand it.
Suppose a designer of a 10 ft. parabolic solar cooker wants to place the cooking pot 5 ft. above the vertex. For reference, the first considers a parabolic string with a base 10 ft. and a focus at 5 ft.from the vertex. How deep is the parabolic solar cooker?
Thank you for your help!
Click here to see answer by ikleyn(52798)

Question 1167082: a flashlight is shaped like a paraboloid so that if its bulb is places at then focus, the light rays from the bulb will then bounce off the surface in a focused direction that is parallel to the x-axis. if the paraboloid has a depth of 1.8 inches and the diameter on its surface is 6 inches, how far should the light source be placed from the vertex
Click here to see answer by ikleyn(52798)

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(407)

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(20850)

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.
Click here to see answer by CPhill(1959)

Question 1168978: Foci at (-1,4) and (7,4), transverse axis has the length 8/3. Whats the equation
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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 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.
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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 1168877: Find the length of latus rectum (LR) is 10, vertex at the origin; parabola opens to the right.
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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

Click here to see answer by MathLover1(20850)

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(52798)

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(1959)

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 htmentor(1343)

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(52798)

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

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