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

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Question 1196491: Radiation is focused to an unhealthy area in a patient's body using a parabolic reflector, positioned in such a way that the target area is at the focus. If the reflector is 30 cm wide and 15 cm deep at the center, how far should the base of he reflector be from the target area?
Click here to see answer by MathLover1(20850)

Question 1196496: Radiation is focused to an unhealthy area in a patient's body using a parabolic reflector, positioned in such a way that the target area is at the focus. If the reflector is 30cm wide and 15 cm deep at the center, how far should the base of the reflector be from the target area?
Click here to see answer by MathLover1(20850)

Question 1196512: A tunnel in parabolic shape is defined by the x^2-16y=0 (dimensions measured in feet). What is its width at the base?
Click here to see answer by Alan3354(69443)

Question 1196512: A tunnel in parabolic shape is defined by the x^2-16y=0 (dimensions measured in feet). What is its width at the base?
Click here to see answer by ikleyn(52795)

Question 1196512: A tunnel in parabolic shape is defined by the x^2-16y=0 (dimensions measured in feet). What is its width at the base?
Click here to see answer by math_tutor2020(3817)

Question 1196658: An elliptical arch bridge is build across a one lane highway. The arch is 20ft across an has a maximum center height of 12ft Will a farm truck hauling a load loft wide with a clearance height of 11ft be able to go through the bridge without damage?
Click here to see answer by Alan3354(69443)

Question 1197082: WW 1.3
Determine whether the equation is a circle or parabola and transform the general equation to standard equation.
If the equation is a circle, you need to identify the center and radius of the circle with the given equation in each item. Sketch
its graph and label the 2 parts of the circle.
If the equation is a parabola, you need to identify the opening, vertex, focus, latus rectums, axis of symmetry and directrix of the parabola. Sketch its graph and label the 6 parts of the parabola.
1. x²+ y²-6x= 7
2. x²+8y8x+40= 0
3.9x2+9y²+54x - 36y + 36 = 0
4. x²-8x - y +9 = 0

Click here to see answer by math_tutor2020(3817)

Question 1197299: Find the differential equation representing ellipses and hyperbolas with
axes on the coordinate axes.
Click here to see answer by Edwin McCravy(20056)

Question 1197335: Find the equation (hyperbola)
foci at ( - 3, 1) and (7,
1) and length of the
transverse axis is 4
units.
Click here to see answer by MathLover1(20850)

Question 1197354: Find the latus rectum in the equation
16x²+25y²+160x+200y+400=0
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Question 1197350: Find the equation (hyperbola)
asymptotes y - 3 = √13/6 (x-2) and focus at (9, 3)

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Question 1197338: Find the equation
asymptotes y - 3 =
± square root of 13/6
(𝑥 − 2) and
focus at (9, 3)
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Question 1197383: 9x^2+4y^2+36x-24y+36=0

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Question 1197383: 9x^2+4y^2+36x-24y+36=0

Click here to see answer by greenestamps(13200)

Question 1197591: What is the vertex of the absolute value function f(X)=- the absolute value of X-5 -3, and does it open up, or down?
Click here to see answer by MathLover1(20850)

Question 1197591: What is the vertex of the absolute value function f(X)=- the absolute value of X-5 -3, and does it open up, or down?
Click here to see answer by greenestamps(13200)

Question 1197630: Describe the end behavior of the function f(x)=3x^6+7x^3+5
Click here to see answer by ikleyn(52795)

Question 1197617: Word Problems (Ellipse)
The planet earth comes closest to the sun at 147 million
km, and farthest from the sun at 152 million km. Thus,
its orbit is an ellipse for which the two vertices are 147
and 152 units away from a particular focus, the sun.
Find the equation of this ellipse, assuming that the major
axis is horizontal and the center at the origin. (units to be
in million km.)
Click here to see answer by MathLover1(20850)

Question 1197655: Find the coordinates of the focus for the parabola y=x^2 + 5x -2
Click here to see answer by ewatrrr(24785)

Question 1197747: Give the standard equation of the circle satisfying the given condition: center at (-4,3), radius sqrt(7).
Click here to see answer by josgarithmetic(39618)

Question 1197747: Give the standard equation of the circle satisfying the given condition: center at (-4,3), radius sqrt(7).
Click here to see answer by ikleyn(52795)

Question 1197808: The entrance to a tunnel under a river is in the shape of a parabola. The width of the tunnel at ground level is 20m . At a distance of 4m from one edge of the tunnel, the height is 16m. Find the height of the tunnel in the middle. Please help!!

Click here to see answer by ikleyn(52795)

Question 1198028: The path of aship can be described by a hyperbolic model centered at the origin, relative to two stations on the shore 168 miles apart that are located at the foci. If the ship is 60 miles south of the center of the hyperbola, find the equation of the hyperbola.

Click here to see answer by MathLover1(20850)

Question 1198113: A beverage container is made of aluminum (SG = 2.7) with a thickness of 0.1 mm.
It's cylindrical, with a top and bottom of Al.
How much water (SG = 1) will produce the lowest center of gravity?
Click here to see answer by Alan3354(69443)

Question 1198114: A beverage container is made of aluminum (SG = 2.7) with a thickness of 0.1 mm.
It's cylindrical, with a top and bottom of Al.
The diameter is 64 mm, the height is 128 mm.
//////////////////////////////
How much water (SG = 1) will produce the lowest center of gravity?
Click here to see answer by ikleyn(52795)

Question 1198212: Find an equation for the parabola that has its vertex at the origin
and has its focus at the point:(8.6,0)
Click here to see answer by MathLover1(20850)

Question 1198215: An arch is in the shape of a parabola. It has a span of 348 feet and a maximum height of 29 feet.
Find the equation of the parabola.
Determine the distance from the center at which the height is 11 feet.
Click here to see answer by MathLover1(20850)

Question 1198403: Find the equation of hyperbola given the conditions:
Vertices: (13,0), (-1,0); asymptotes: y = x - 6 and y = -x + 6
Click here to see answer by MathLover1(20850)

Question 1198410: natural draft cooling tower are shaped like hyperbola for more efficient cooling of power plants. The hyperbola in the tower can be modeled by x^2 over 25 minus y^2 over 256 equals to 1 with 150m as its height. Find the width of the tower at the top and its narrowest part in the middle.
Click here to see answer by MathLover1(20850)

Question 1198407: natural draft cooling tower are shaped like hyperbola for more efficient cooling of power plants. The hyperbola in the tower can be modeled by x^2 over 25 minus y^2 over 256 equals to 1 with 150m as its height. Find the width of the tower at the top and its narrowest part in the middle.
Click here to see answer by ikleyn(52795)

Question 1198510: Determine the type of conic section represented by the equation
(X+6)^2/25 - (y+4)^2/64 = 1
The answer is one of the following. Which one?
A) hyperbola
B) ellipse
C) parabola
D) line
E) circle

Click here to see answer by ikleyn(52795)

Question 1198611: standard equation (x-h)^2=4p(y-k) of (3x-2)^2=84y-12
Click here to see answer by greenestamps(13200)

Question 1198612: give the standard equation of (3x-2)^2=84y-12. Provide it's vertex, focus, directrix, axis of symmetry, latus rectum and endpoints of latus rectum.
Click here to see answer by MathLover1(20850)

Question 1198621: how to graph the major axis = 186,014, 000 miles and minor axis = 185, 987, 932.9 miles.
Click here to see answer by MathLover1(20850)

Question 1198620: how to convert the major axis = 186,014, 000 miles and minor axis = 185, 987, 932.9 miles into a general form or standard form?
Click here to see answer by mccravyedwin(407)

Question 1198938: Consider the elipse 9x^2 + 36y^2=324.
Which of the following statements about the foci and eccentricity is correct?
A) the foci are [(0,-3(square root of 3)] and [(0,3(square root of 3)], and the eccentricity is (1/2)(square root of 3)
B) the foci are [(0,-3(square root of 3)] and [(0,3(square root of 3)], and the eccentricity is square root of 3
C) the foci are [(-3(square root of 3), 0] and [(3(square root of 3),0], and the eccentricity is (1/2)(square root of 3)
the foci are [(0,-3(square root of 3)] and [(0,3(square root of 3)], and the eccentricity is (1/2)(square root of 3)
D) the foci are [(-3,(square root of 3),0] and [(3(square root of 3),0], and the eccentricity is square root of 3
Click here to see answer by Edwin McCravy(20056)

Question 1198937: Consider the elipse 9x^2 + 36y^2=324
Which of the following statements about the vertices is correct?
A) the vertices on the major axis are (-3,0) and (3,0), and the vertices on minor axis are (0,-6) and (0,6)
B) the vertices on the major axis are (0,-6) and (0,6), and the vertices on minor axis are (-3,0) and (3,0)
C) the vertices on the major axis are (0,-3) and (0,3), and the vertices on minor axis are (-6,9) and (6,0)
D) the vertices on the major axis are (-6,0) and (6,0), and the vertices on minor axis are (0,-3) and (0,3)
Click here to see answer by MathLover1(20850)

Question 1199102: Consider the parabola y=x^2 +4x-3. Find the equation of the directrix.
One of the following is correct. Which one is correct?
A) y=-7
B) y=-7.25
C) y=-8
D) y=-7.75
Click here to see answer by greenestamps(13200)

Question 1199101: Consider the parabola y=x^2 +4x -3.
Find the coordinates of the focus.
The correct answer is one of the following. Which one is correct?
A) (-2,-6.75)
B) (2,6.75)
C) (-2,-6)
D) (-2,-5.75)
Click here to see answer by greenestamps(13200)

Question 1199204: f(x)=x^2+x-2
put the equation in vertex form
determine the vertex point
deter,ine the x-intercept the y-intercept, and the axis of symmetry

Click here to see answer by MathLover1(20850)

Question 1199413: a parkway 80 feet wide is spanned by a parabolic arch 100 feet long along the horizontal. if the parkway is 60 feet wide, the minimum clearance 15 feet and the parabolic arch is 25 feet high, how long is the arch?
Click here to see answer by ikleyn(52795)

Question 1199412: find the equation of a parabola with vertex on the line y=2x, axis parallel to the y axis and passing through (3/2, 1) & (3,4)
Click here to see answer by ikleyn(52795)

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