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

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Question 1191212: Vertex at the origin, opens to the right, focus = (-4,0)
Click here to see answer by josgarithmetic(39620)

Question 1191321: Find the polar coordinates of all 8 vertices of a regular octagon if the center is at the pole and one vertex is on the x-axis a distance of "m" away from the center.
Click here to see answer by math_tutor2020(3817)

Question 1191565: Find two nonnegative numbers whose sum is 12 such that their
product is an absolute maximum.
Click here to see answer by Alan3354(69443)

Question 1191565: Find two nonnegative numbers whose sum is 12 such that their
product is an absolute maximum.
Click here to see answer by Edwin McCravy(20060)

Question 1191565: Find two nonnegative numbers whose sum is 12 such that their
product is an absolute maximum.
Click here to see answer by greenestamps(13200)

Question 1191566: Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a right-circular cone with a radius of 5 cm and a height of 12 cm.
Click here to see answer by greenestamps(13200)

Question 1191567: In the planning of a coffee shop, the daily profit is estimated to be $16 per place if there are places for 40 to 80 people. However, if the seating capacity is more than 80 places, the daily profit on each place will be decreased by $0.08 times the number of places above 80. What should be the seating capacity to yield the greatest daily profit?
Click here to see answer by Theo(13342)

Question 1191935: What acute angle does a line with slope -3/2 make with a vertical line? Write answer in decimal
form.
Click here to see answer by ikleyn(52803)

Question 1191934: A line passes through A(-2, 1) and B(3, 4). Find the point P on AB extended through B so that P is twice as far from A as from B. (b) the point Q on AB extended through B so that P is twice as far from B as from A.
Click here to see answer by ikleyn(52803)

Question 1191936: The points A(-2, 3), B(6, -5) and (8, 5) are vertices of a triangle. Find the equations of its
medians.
Click here to see answer by math_helper(2461)

Question 1191933: Find the equation of the circle tangent to the line 5x + y = 3 at the point (2, -7) and the center is
on the line x - 2y = 19.
Click here to see answer by Alan3354(69443)

Question 1191933: Find the equation of the circle tangent to the line 5x + y = 3 at the point (2, -7) and the center is
on the line x - 2y = 19.
Click here to see answer by Edwin McCravy(20060)

Question 1191931: Find the equation of a circle tangent to the line 3x - 4y = 34 at the point (10, -1) and also
tangent to the line 4x + 3y = 12 at the point (3, 0).
Click here to see answer by Alan3354(69443)

Question 1192145: Center at (0, 0), transverse axis along the y-axis, passing through the points (5, 3) and (-3, 2).
Click here to see answer by Solver92311(821)

Question 1192204: Determine the nature of the following degenerate conics

Click here to see answer by ikleyn(52803)

Question 1192552: In a figure, curve A whose equation is y=(x+a)^2, passes through the point (4,0).
Curve B whose equation is y=(x+a)^2+b, passes through the point (4,-9).
a)Calculate the values of a and b
b)if the curve B intersects the x-axis at point (p,0) and (q,0), calculate the values of p and q
c)if curve B intersects the y-axis at the point (0,r), calculate the value of r.
Click here to see answer by Boreal(15235)

Question 1193003: Given the hyperbola with the equation y^2 -9x^2 =-9
find the vertices, the foci, and the equations of the asymptotes.
Click here to see answer by Edwin McCravy(20060)

Question 1193536: 1. Find an equation of a circle passing through the points A(1,2) and B(1,-2) touching the line x+2y+5=0.
2. Find the center and radius of 5x^2+5y^2+24+36y+10=0
Click here to see answer by Alan3354(69443)

Question 1193657: What does the line y = 4 - 1/(1 * 151) represent in y = 5 * (x - 3) ^ 2 + 4

Click here to see answer by greenestamps(13200)

Question 1193657: What does the line y = 4 - 1/(1 * 151) represent in y = 5 * (x - 3) ^ 2 + 4

Click here to see answer by math_tutor2020(3817)

Question 1193860: Find the general equation of the ellipse whose major axis is 20 units and the foci are
the points of coordinates (0, 5√3) and (0, −5√3).
Click here to see answer by ikleyn(52803)

Question 1194067: The vertices of a hyperbola are the points (−3, 2) and (−3, −2) and the length of its conjugate is 6.
Find the equation of the hyperbola, the coordinates of its foci, and its eccentricity.
Click here to see answer by ikleyn(52803)

Question 1194068: Find the equation of the horizontal hyperbola that has its center at (0,0), its straight side is 6
units and its eccentricity is √7/2.
Click here to see answer by MathLover1(20850)

Question 1194079: Halle la ecuación canónica de la hipérbola que tiene sus Focos en (±3,0) y lado recto |𝐿R| = 5
Click here to see answer by MathLover1(20850)

Question 1194078: Find the canonical equation of the hyperbola that has its Foci at (±3,0) and straight side |SS| = 5

Click here to see answer by MathLover1(20850)

Question 1194243: Find the equation of the line with slope 𝑚 = 2/3, passing through the point (0, −5).
Click here to see answer by MathLover1(20850)

Question 1194243: Find the equation of the line with slope 𝑚 = 2/3, passing through the point (0, −5).
Click here to see answer by MathTherapy(10552)

Question 1194244: A record company makes an initial investment of $5,000 to prepare songs for a
Musical Album. The cost of manufacturing and recording each disc is 4 dollars. Furthermore, the discography
must pay the singer $1 per record for copyright. It is decided that the selling price
of the disc is 15 dollars.
a. Determine the profit function of the company based on the records sold.
b. Find the balance point.
c. Determine the number of records that must be sold for the company to make a profit.
of $100,000.
d. What are the profits if only 200 discs are sold?
Click here to see answer by math_tutor2020(3817)

Question 1194247: La relación entre la temperatura del aire
T
(en °F) y la altitud
h (en pies sobre el nivel del mar) es
aproximadamente lineal para
0 ≤ h ≤ 20000
. Si la temperatura al nivel del mar es 60°𝐹, un aumento
de 5000 pies en altitud baja la temperatura del aire en alrededor de 18°𝐹.
a) Exprese
T
en términos de
h
y trace la gráfica en un sistema de coordenadas.
b) Aproxime la temperatura del aire a una altitud de 15 000pies.
c) Aproxime la altitud a la que la temperatura sea 0°𝐹.
Click here to see answer by MathLover1(20850)

Question 1194267: In a laboratory experiment, it is observed that when the temperature is reduced 𝑇 (degrees Celsius) of a rabbit, its heart rate (beats per minute) decreases. Under laboratory conditions, a rabbit at a temperature of 37°𝐶 has a heart rate of 220 and at a temperature of 32°𝐶 its heart rate heart rate decreases to 150. The function 𝑅 is heart rate and is linearly related to the temperature 𝑇. a) Find the functional relationship between 𝑅 and 𝑇 and its respective graph. b) Find the variation of 𝑅 if 𝑇 = [26, 38].
Click here to see answer by math_tutor2020(3817)

Question 1194268: En un experimento de laboratorio, se observa que cuando se reduce la temperatura 𝑇 (grados Celsius)
de un conejo, su ritmo cardíaco (latidos por minuto) disminuye. En condiciones de laboratorio, un
conejo a temperatura de 37°𝐶 tiene un ritmo cardíaco de 220 y a una temperatura de 32°𝐶 su ritmo
cardíaco disminuye a 150. La función 𝑅 es ritmo cardíaco y está relacionada linealmente con la
temperatura 𝑇.
a) Encontrar la relación funcional entre 𝑅 y 𝑇 y su respectiva gráfica.
b) Hallar la variación de 𝑅 si 𝑇 = [26, 38].
Click here to see answer by josgarithmetic(39620)

Question 1194328: Find the distance between two points. (-2,-1) (3,5)
Click here to see answer by Alan3354(69443)

Question 1194328: Find the distance between two points. (-2,-1) (3,5)
Click here to see answer by josgarithmetic(39620)

Question 1194361: 3x^2+2y^2=30
2x^2-5y^2=-37
Click here to see answer by Alan3354(69443)

Question 1194364: Find the center, vertices, and foci of the ellipse for 4x^2+25y-8x+ 100y+4=0. Solve and graph
Click here to see answer by ikleyn(52803)

Question 1194408: Graph the function: f(x)= 3x+5/2x-6 indicating: asymptoms, domain and range
Click here to see answer by ikleyn(52803)

Question 1194408: Graph the function: f(x)= 3x+5/2x-6 indicating: asymptoms, domain and range
Click here to see answer by greenestamps(13200)

Question 1194409: Suppose the trajectory of a javelin throw is parabolic and can be described by the equation: 200y = 80x - x^2, where x is the horizontal distance, "y" is the height. Both measurements are in meters. What is the mark reached?
Click here to see answer by ikleyn(52803)

Question 1194414: Assume that the trajectory in a javelin throw is parabolic and that it can be described
using the equation:
200𝑦 = 80𝑥 − x^2
where 𝑥 is the horizontal distance, 𝑦 is the height. Both measurements are in meters. what is the brand
reached?
Click here to see answer by Alan3354(69443)

Question 1194412: 2. Find the domain, range, and asymptotes (if any) of the following functions:
a) 𝑓(𝑥) = 4𝑥+3/𝑥+2
b) 𝑓(𝑥) =𝑥+2/𝑥^2−1
c)𝑓(𝑥)=𝑥2−4𝑥+5/𝑥−3
Click here to see answer by MathLover1(20850)

Question 1194411: Find the domain, range, and asymptotes (if any) of the following functions:
a) f(x)= 4x+3/ x+2
b) f(x)= x+2/ x^2-1
Click here to see answer by MathLover1(20850)

Question 1194456: A comet follows a hyperbolic path in which the sun is located at one of its foci. The path of the comet can be modeled by the hyperbola shown below, centered at the origin and opening left/right. If the closest distance the comet reaches to the sun is 160 million km, and the sun is 325 million km from the center of the hyperbola, write an equation of the hyperbola (in millions of km).
Click here to see answer by ikleyn(52803)

Question 1194362: Find the vertex, focus, and directrix of the parabola X^2-4X- 4Y +16=0. Solve and graph
Click here to see answer by josgarithmetic(39620)

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