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

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Question 1166898: Write the standard equation of the ellipse with the given properties
Horizontal major axis of length 10, center at the origin, and passes through ( 3,16/5 )
F_1 (-7,-3),F_2 ( -1,-3) and V_1 (1,-3)
C(0,0), a vertex is 8 units from a focus and 18 units from the other
F_1 (-4,0),F_2 ( 4,0) and passing through (4,1)

Click here to see answer by Edwin McCravy(20059)

Question 1166903: A toy rocket is launched in an open field. The path of the rocket can be modelled by the relation h=-5(t-3)^2+68.
h= height in meter above the ground
t= the time after the rocket was launched in seconds
what is the maximum height that the rocket reaches?
how long does it take the rocket to reach its maximum height?
Click here to see answer by ikleyn(52798)

Question 1166895: For the given ellipse, find the principal axis, center, vertices, co-vertices, foci, length of the major axis and length of minor axis
5y^2+2x^2=10
(x+2)^2/25+(y+5)^2=1

Click here to see answer by Edwin McCravy(20059)

Question 1167066: what is standard equation of center origin contains (0,-3) in circle

Click here to see answer by josgarithmetic(39620)

Question 1167019: A whispering gallery has a semielliptical ceiling that is 9 m high and 30 m long. How high is the ceiling above the two foci? Also, find the distance of the focus from the center, equation of the ellipse, and answer to the problem.
Click here to see answer by greenestamps(13200)

Question 1167018: A tunnel has the shape of a semi ellipse that is 15 ft high at the center, and 36 ft across at the base. At most how high should a passing truck be, if it is 12 ft wide, for it to be able to fit through the tunnel?
Click here to see answer by greenestamps(13200)

Question 1167133: 4x^2+12x+4y^2+16y-11=0

Click here to see answer by josgarithmetic(39620)

Question 1167133: 4x^2+12x+4y^2+16y-11=0

Click here to see answer by MathTherapy(10552)

Question 1167133: 4x^2+12x+4y^2+16y-11=0

Click here to see answer by ikleyn(52798)

Question 1167133: 4x^2+12x+4y^2+16y-11=0

Click here to see answer by Alan3354(69443)

Question 1167132: A ladder of length 15m moves with its end always touching the vertical wall and horizontal floor.determine the equation of the locus of a point p on the ladder which is 6m from the end of the ladder in contact with the floor.
Click here to see answer by ikleyn(52798)

Question 1167130: A girder of a railway bridge is in the parabolic form (open downward) with span looft and the height point on the arch is left above the bridge.find the height of the bridge at 10 feet to the left or right from the midpoint of the bridge.
Click here to see answer by ikleyn(52798)

Question 1167131: A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 9mts.if the distance across (diameter)& the top of the mirror is 160cm.how deep is the mirror at the middle?
Click here to see answer by ikleyn(52798)

Question 1167218: kelly and her friends agreed to share internet connection with one another. they placed the router at the center of their dorm. the router has a range of 15 meters. joana’s room is located 5 meters east and 5 meters north of the router. cherry’s room is located 10 meters east and 15 meters south of the router. kelly’s room is located 5 meters west, and 10 meters north of the router, and bella’s room is located 10 meters south of the router. who among them has no access to the internet connection?

Click here to see answer by ikleyn(52798)

Question 1167217: kelly and her friends agreed to share internet connection with one another. they placed the router at the center of their dorm. the router has a range of 15 meters. joana’s room is located 5 meters east and 5 meters north of the router. cherry’s room is located 10 meters east and 15 meters south of the router. kelly’s room is located 5 meters west, and 10 meters north of the router, and bella’s room is located 10 meters south of the router. who among them has no access to the internet connection?

Click here to see answer by Theo(13342)

Question 1167083: The tower supporting the cable of suspension bridge are 1200 meters apart and 170 meters above the bridge it supports.Suppose the cable hangs, following the shape of a parabola, with its lowest point 20 meters above the bridge. How high is the cable 120 meters away from the tower?
Click here to see answer by htmentor(1343)

Question 1167286: A router is in the library of the university which is 1.5 meters 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 Theo(13342)

Question 1167417: Find the equation of the hyperbola (in standard and general forms) which satisfies the conditions given.
Foci at (2-√13,3) and (2+√13,3), vertices at (5,3) and (-1,3)
Click here to see answer by Edwin McCravy(20059)

Question 1167632: Find the equation of a parabola with axis parallel to the x-axis and
passing through (3/2, 1), (5, 0) and ( - 1, 2).
Click here to see answer by Boreal(15235)

Question 1167613: The owner of an animal farm who happens to be an architect is trying to design a parabolic arch of the entrance to his farm. He wants the highest point of the arch to be 10ft from the ground. Also included in his design is that at the height of 8ft the width of the arc is to be 6ft. How wide does he want the arch at ground level?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1167661: Write the standard equation of the parabola given the two endpoints of
the focal width ; (-2,3) and (5,3) with p>0
Click here to see answer by Edwin McCravy(20059)

Question 1167982: Find the vertex and directrix of
2x^2+4y-8=0
Click here to see answer by josgarithmetic(39620)

Question 1168154: the end points of the major and minor axed of an ellipse

Click here to see answer by greenestamps(13200)

Question 1168160: The reflective property of hyperbolas Show that a ray of light directed toward one focus of a hyperbolic mirror, as in the accompanying figure, is reflected toward the other focus. (Hint: Show that the tangent to the hyperbola at P bisects the angle made by segments PF1 and PF2

Click here to see answer by ikleyn(52798)

Question 1168162: the endpoints of major and minor axes of an ellipse are (1,1),(3,4),(1,7)and(-1,4).sketch the ellipse give the question in standard form and find its foci eccentricity and directrices
Click here to see answer by solver91311(24713)

Question 1168419: The parabola has a vertex of (1,4) and a directrix y= 5 write an equation of the conic parabola.
Click here to see answer by josgarithmetic(39620)

Question 1168585: Find the equation of parabola in standard form having the given properties
a. Vertex at (2,4), focus at (-3,4)
Click here to see answer by htmentor(1343)

Question 1168614: Find an equation of the parabola in standard form having the given properties. Draw a sketch of the parabola ( make sure to emphasize all of the properties of the parabola)
A. vertex at (2,4), focus at (-3,4)
B. vertex at origin, opens upward, length of latus rectum is 4 units
Click here to see answer by josgarithmetic(39620)

Question 1168620: Find an equation of the parabola in standard form having the given properties. Draw a sketch of the parabola ( make sure to emphasize all of the properties of the parabola)
A. vertex at (2,4), focus at (-3,4)
B. vertex at origin, opens upward, length of latus rectum is 4 units
Click here to see answer by josgarithmetic(39620)

Question 1168623:
Click here to see answer by josgarithmetic(39620)

Question 1168718: A flashlight is like a praboloid, so that if it's 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 1.8 inches and the diameter on it's surface is 6 inches, how far should the light source be placed from the vertex

Click here to see answer by htmentor(1343)

Question 1168541: The arch of the bridge forms from the upper half of the bridge forms the upper half of an ellipse. The highest point of the arch is 6m above the 20m wide river. Write the equation of the ellipse in which the major axis coincides with the water level.
Click here to see answer by ikleyn(52798)

Question 1168801: 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)=−4x^2, but with the given maximum or minimum.
Maximum=7 at x=-2

Click here to see answer by MathLover1(20850)

Question 1168851: Please help me solve this problem. Center in the third quadrant, tangent to both the x-axis and y-axis, radius 8. Thank you
Click here to see answer by josgarithmetic(39620)

Question 1168875: Find the equation of the parabola is: directrix y-5=0, vertex (0, 0).

Click here to see answer by htmentor(1343)

Question 1168876: Axis along x-axis; vertex at the origin, passing through (2, 5), find the equation of the parabola.
Click here to see answer by josgarithmetic(39620)

Question 1168874: Find the equation of the parabola is: vertex (0, 0); focus (4, 0).
Click here to see answer by josgarithmetic(39620)

Question 1168935: A 10ft tall, 10ft 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 15ft at the center and a base of 12ft wide. Will the truck be able to fit through the arch? Identify the equation that will model the given situation.
Click here to see answer by Solver92311(821)

Question 1169046: Aunt Barbara has a doorway in the shape of a parabola. Find an equation describing the door given that is 4 feet across and 8 feet high in the center. Determine the width of the doorway at a point 5 feet off the ground.
Click here to see answer by Solver92311(821)

Question 1169050: Please help me with this.Finding the equation of ellipse.Given endpoints of major axis are (-4,3)and (8,3),one end of the minor axis (2,5). Thank you in advance well appreciated😊😊
Click here to see answer by htmentor(1343)

Question 1169049: Please help me with this.Finding the equation of ellipse given the center(2,-3) major axis 16,focus (2,3)

Click here to see answer by greenestamps(13200)

Question 1169029: Two control towers are located at points Q(-400,0) and R(400,0), on a straight shore
where the x-axis runs through (all distances are in meters). At the same moment, both
towers sent a radio signal to a ship out at sea, each traveling at 250 m/µs. The ship
received the signal from Q 2.9 µs (microseconds) before the message from R. Find the
equation of the curve containing the possible location of the ship.
Click here to see answer by htmentor(1343)

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