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

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Question 1199404: A basketball player want to hit 3 points to win the tournament. To do that, he
need to hit three point at the coordinates of the latera recta in his courtside. The
basketball player court is at the left side of the figure below. The available data
he have: Center of the court (0, 0); center of the three point line from the base
line, 21ft; center of the free throw line from the base line, 15 ft. Foci is at (-27,0)
and (27,0) and Vertices are at (-21,0) and (21, 0) respectively. What is the
coordinate of the Latera Recta at the left side of the court for him to shoot the
championship shot?
Click here to see answer by ikleyn(52795)

Question 1199474: find the following:Semi-Transverse length a, Semi-Conjugate length b,Vertices,Co-Vertices and Foci of 9x^2-4y^2-36x+8y=4
Click here to see answer by mccravyedwin(407)

Question 1199474: find the following:Semi-Transverse length a, Semi-Conjugate length b,Vertices,Co-Vertices and Foci of 9x^2-4y^2-36x+8y=4
Click here to see answer by Edwin McCravy(20056)

Question 1199546: Given the hyperbola xy = 1. Determine the new equation of this hyperbola if the x,y axes are rotated about the origin by 45 degrees clockwise.
Answer: y^2 - x^2 = 2
Click here to see answer by htmentor(1343)

Question 1199585: The towers of a 60 meter parabolic suspension bridge are 12 m high and the lowest point of the cable is 3 m above the roadway. Find the vertical distance from the roadway to the cable at 15 m from the center.
A. 3 m
B. 6 m
C. 5 m
D. 8 m
Click here to see answer by ikleyn(52795)

Question 1199589: Determine the distance from the curve x^2 + y^2 - 16y + 16x + 64 = 0 to point (6,4).
A. 6.56
B. 5.24
C. 7.52
D. 4.16
Click here to see answer by ikleyn(52795)

Question 1199599: Alpha particles are deflected along the hyperbolic paths when they
are directed towards the nuclei of gold atoms. If an alpha particle
gets as close as 12 units to the nucleus along the hyperbolic path
with asymptotes of 𝑦 = 5x/12, what is the equation of its path.
Assume that the transverse axis is on y-axis. Illustrate the said path
taken by the alpha particles. Illustrate the path taken by the alpha
particles.

Click here to see answer by ikleyn(52795)

Question 1199626: How does the graph of the hyperbola whose equation is (y2)/4 - (x2)/9 = 1 open?
A. A hyperbola does not open.
B. Hyperbola opens to the sides.
C. Hyperbola opens toward its vertices.
D. This graph is not a hyperbola.
E. Hyperbola opens toward its center.
F. Hyperbola opens up and down.
Click here to see answer by ikleyn(52795)

Question 1199622: The parametric equation of a curve is 𝑥 = h + 𝑎 sec 𝑡 , 𝑦 = 𝑘 + 𝑏 csc 𝑡. By eliminating the parameter t, it can be demonstrated that the curve is
A) a circle B) an ellipse C) a parabola D) a hyperbola E) a cycloid
Click here to see answer by Edwin McCravy(20056)

Question 1199625: How does the graph of the hyperbola whose equation is (x2)/9 - (y2)/25 = 1 open?
A. A hyperbola does not open.
B. This graph is not a hyperbola.
C. Hyperbola opens to the sides.
D. Hyperbola opens toward its center.
E. Hyperbola opens up and down.
F. Hyperbola opens toward its vertices.
Click here to see answer by Edwin McCravy(20056)

Question 1200121: Find the equation of the parabola with axis parallel with the x-axis and passing through (4,2), (-4,10) and (-4, -6). Sketch the graph
Click here to see answer by josgarithmetic(39618)

Question 1200120: Given the line 𝑥 + 2𝑦 − 4 = 0 and circle 𝑥^2 + 𝑦^2 − 8𝑥 − 4 = 0, find the equations of the tangents to the circles which are perpendicular to the line. Sketch the graph.
Click here to see answer by ikleyn(52795)

Question 1200122: Find the point on the ellipse 𝑥^2 + 5𝑦^2 = 36 which is the closest, and which is the farthest point from the line 2𝑥 − 5𝑦 + 30 = 0. Sketch the graph
Click here to see answer by Edwin McCravy(20056)

Question 1200276: Identify the graph using co-ordinate geometry. Where are the vertex and focus located? What is the equation of the directory?
〖(y+2)〗^2=8(x-1)

Click here to see answer by math_tutor2020(3817)

Question 1201025: I do not understand how to do this. Please help me.
The vertex of this parabola is at (1, -4). When the y-value is -5, the x-value is 4. What is the coefficient of the squared term in the equation of this parabola?
Click here to see answer by greenestamps(13200)

Question 1201024: The vertex of this parabola is at (1, 2). When the x-value is 0, the y-value is 0. What is the coefficient of the squared term in the equation of this parabola?
I don't know where or how to start, please help me.
Click here to see answer by josgarithmetic(39618)

Question 1201149: Find the standard form of the equation of each ellipse.
14. Major axis horizontal with length 12; length of minor axis 4; center: (−1, 3)
Click here to see answer by ikleyn(52795)

Question 1201669: Plotting graph for y=3x-x^2
Click here to see answer by Theo(13342)

Question 1201669: Plotting graph for y=3x-x^2
Click here to see answer by mananth(16946)

Question 1201708: find an equation of the ellipse that has a center (2,5), a major axis of length 12, and endpoint of minor axis (2,3)
Click here to see answer by greenestamps(13200)

Question 1201701: The equation of a parabola is 12 y = ( x − 1 ) 2 − 48 12y=(x-1)2-48 . Identify the vertex, focus, and directrix of the parabola. 
Click here to see answer by greenestamps(13200)

Question 1201814: A florist spent $1558 purchasing 64 bundles of flowers to make spring bouquets. The order consisted of tulips, daisies, and peonies. The peonies cost $95 a bundle, the tulips were $23 a bundle adn the daisies were $12 a bundle. The florist purchased the fewest bundles of peonies, and twice as many daisies as tulips.
a. Write a system of equations to represent the information, solve the system using elimination or substitution, and then determine the number of bundles of each flower.
Click here to see answer by ikleyn(52795)

Question 1201817: A whispering gallery allows a whisper in one area to be heard plainly in a second area. A whispering gallery with an elliptical shape is built so that the person standing at one focus of the ellipse can whisper and be heard by another person standing at the other focus. The gallery will be 150 feet in length and 42 in width. A view from above is shown in the diagram.
a. What is the equation of the ellipse used to represent the outline of the room?
b. If two secret keepers are standing at the foci of the room to hear each other whisper, how far apart are they? Round to the nearest foot.
Click here to see answer by ikleyn(52795)

Question 1201815: On March 8th, 2017, the Azure Window, a natural rock formation located on the island of Gozo in Malta, collapsed. The arch was parabolic with a height of approximately 80 feet and a span of 64 feet at the waterline. Use this information to solve for p.
a. the approximate foci of the arch and give an equation that models the arch.
Click here to see answer by ikleyn(52795)

Question 1202100: A dog trainer has 100 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 504 ft2, what will be the dimensions of the work area?
Click here to see answer by josgarithmetic(39618)

Question 1202156: 9x^2+4y^2-90x+16y+250=0
Click here to see answer by greenestamps(13200)

Question 1202288: the orbit of mercury around the sun forms an ellipse with eccentricity 0.206,length of the major axis 1.16*10^8km and the sun at one focus. what is the aproximate distance from mercury to the sun?
Click here to see answer by Alan3354(69443)

Question 1202586: x²-14x+10y+79=0
Click here to see answer by greenestamps(13200)

Question 1202586: x²-14x+10y+79=0
Click here to see answer by josgarithmetic(39618)

Question 1202586: x²-14x+10y+79=0
Click here to see answer by ikleyn(52795)

Question 1202858: Find the vertex, focus, and the directrix of the parabola 𝑦2 − 4𝑦 + 4𝑥 + 4 = 0
Unsure I solved the equation.
𝑦2 − 4𝑦 + 4𝑥 + 4 = 0
𝑦2 − 4𝑦 + 4𝑥 + 4−4𝑥 − 4 = 0 −4𝑥 − 4
− 𝑦2 − 4𝑦 =−4𝑥 - 4
− 𝑦2 − 4𝑦 + 4 =−4𝑥 − 4 + 4
(y−2)² = −4x
(y−2)² = 4(−1)(x−0)
Horizontal Parabola (opens left)
(y−k)² = 4p(x−h)
Vertex (0, 2)
Focus (−1, 2)
Directrix = 1
p = −1

Click here to see answer by josgarithmetic(39618)

Question 1202880: Opens to the right, length of the latus rectum = 6, and passing through
(2/3, 0) and (- 1/2, 7)
Click here to see answer by Edwin McCravy(20056)

Question 1203004: The function f is graphed in the xy-plane. If y=f(x) and y=k, what are the three real solutions for -5 is less than or equal to x which is less than or equal to 15
Click here to see answer by greenestamps(13200)

Question 1203574: Vertex (3,2) and Focus at (4,2)
Click here to see answer by josgarithmetic(39618)

Question 1203574: Vertex (3,2) and Focus at (4,2)
Click here to see answer by ikleyn(52795)

Question 1203574: Vertex (3,2) and Focus at (4,2)
Click here to see answer by greenestamps(13200)

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