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

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Question 1144268: Find an equation of the line containing the centers of the two circles.
X^2+y^2+6x+4y+12=0
X^2+y^2-2x+10y+22=0
Click here to see answer by ikleyn(52798)

Question 1144425: Determine the vertex,focus,endpoints of Latus rectum, directrix and axis of symmetry of the parabola with given equation y^2=4(x-1)

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Question 1144475: The graph of x^2+y^2+6x-24y+72=0 & x^2-y^2+6x+16y-46=0 intersect at four points. Compute the sum of distance from these four points from the point (-3,2).
Click here to see answer by Alan3354(69443)

Question 1144984: A rectangular piece of property measures 10 miles by 8 miles. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides
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Question 1146215: A circle with center (4 5)pass through y the intercept of the line 5x-2y+6=0 find it equationf
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Question 1146376: Find the equation of the line that is tangent to the point of contact of the circles x2 + y2 + 2x - 4y -20 = 0 and x2 + y2 - 10x + 5y + 25 = 0.
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Question 1146374: Find the equation of the parabola with horizontal axis which crosses the x - axis at x = 2, and the y - axis at y = -1 and y = 7.
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Question 1146375: Given a circle of radius of 4 and center at (6, 8). Find the locus of the center of all circles that is tangent to the x - axis and the given circle.
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Question 1146864: A window is to be constructed in the shape of an equilateral triangle on top of a rectangle if its perimeter is to be 600 cm, What is the maximum possible area of the window?

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Question 1147040: Write the equation of tangent to
3x^2+4y^2-2x+6y-25=0 at point (3,2)
Click here to see answer by Alan3354(69443)

Question 1147041: Write the equation of tangent to
3x^2+4y^2-2x+6y-25=0 at line 2y-8x=0
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Question 1147600: A conic has an equation of x^2 + 4x + 16y = 44, find the coordinates of the focus, vertex, and equation of directrix.
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Question 1147614: Determine the equation of a parabola where the vertex is (4,3) and focus is at (4,-1).

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Question 1147599: Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points (3, 1), (0, 0), and (8,-4)
Click here to see answer by Edwin McCravy(20059)

Question 1148112: what is the equation of a circle passing through (12,1) and (2,-3) with center on the line 2x-5y+10=0
Click here to see answer by ikleyn(52798)

Question 1148688: Given the equation of the parabola: 𝑦^2−8𝑥−4𝑦−20=0. The length of its latus rectum is:

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Question 1148737: The vertex is (-3,-4) and the parabola opens down
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Question 1148737: The vertex is (-3,-4) and the parabola opens down
Click here to see answer by josgarithmetic(39620)

Question 1149108: Find the center and radius of the circle with equation (x - 6)2 + (y + 5)2 = 9
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Question 1149387: foci: (+/-3sqrt(5), 0)
x intercepts: (+/-9,0)
write an equation for Elipses
Click here to see answer by greenestamps(13200)

Question 1149939: Write an equation for the given ellipse that satisfies the following conditions.
Center at (1,1); minor axis vertical, ,with length8; c=3

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Question 1149941: Find an equation for the collection of points for which the distance to (18, 0) is twice the distance to the line x = -18.
Click here to see answer by Edwin McCravy(20059)

Question 1149938: Find the equation of an ellipse satisfying the given conditions.
Foci: (-2,0) and (2,0); length of major axis: 8
Click here to see answer by greenestamps(13200)

Question 1149937: Write an equation for the ellipse with x intercepts (8,0) and (-8,0) and y intercepts (0,7) and (0,-7)
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Question 1149909: Common tangents are drawn to parabola y²=4x and ellipse 3x²+8y²=48 touching the parabola at A & B and the ellipse at C & D.Find the area of quadrilateral
Click here to see answer by Edwin McCravy(20059)

Question 1149990: Write an equation for the hyperbola that has eccentricity 3, center at (0,0), and vertex at (0,8)
An equation for the hyperbola is...?
Click here to see answer by MathLover1(20850)

Question 1149989: Find the standard form of the equation of the hyperbola satisfying the given conditions.
x-intercepts (0,24) and (0,-24). foci at (-26,0) and (26,0)
The equation in standard form of the hyperbola is..
Click here to see answer by MathLover1(20850)

Question 1150009: A one-way road passes under an overpass in the shape of half an ellipse, 15 ft high at the center and 20 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can pass under the overpass?
Click here to see answer by ikleyn(52798)

Question 1150069: An arch is in the shape of a parabola. It has a span of 180 meters and a maximum height of 15 meters. What is the equation of the parabola?
Please and thank you, I'm totally stumped
Click here to see answer by ikleyn(52798)

Question 1150068: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 60 feet across at its opening and 5 feet deep at its center, where should the receiver be placed?
How do you find the equation for this parabola?
Click here to see answer by ikleyn(52798)

Question 1150067: I have a problem "The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tower is 272 feet. The smallest diameter of the tower is 152 which is 366 feet above the ground. The tower is 522 feet tall."
What is the width of the tower at a height of 56 feet?
Click here to see answer by greenestamps(13200)

Question 1150044: Find the standard form of the equation of the hyperbola satisfying the given conditions.
x-intercepts (0,24) and (0,-24). foci at (-25,0) and (25,0)
The equation in standard form of the hyperbola is..
Click here to see answer by greenestamps(13200)

Question 1150091: identity the conic whose equation is 9x²-10xy-4y²-36=0 by rotating the xy-axes to put the conic in standard position.

Click here to see answer by Edwin McCravy(20059)

Question 1150584: the graph has one line on the left side of the graph and it goes through -1. and a ring shape that starts from 10 and loops to -7
Click here to see answer by ikleyn(52798)

Question 1150746: A parabola with equation y = x^2 + bx + c passes through the points (2,3) and (4,3). What is c?
Click here to see answer by ikleyn(52798)

Question 1150746: A parabola with equation y = x^2 + bx + c passes through the points (2,3) and (4,3). What is c?
Click here to see answer by Edwin McCravy(20059)

Question 1150766: if p(x+y) = 2x² +3y², and q(x+y)=4x-18y-39, where x and y are real numbers, what is the minimum value of p(x+y)-q(x+y)?
Click here to see answer by ikleyn(52798)

Question 1150766: if p(x+y) = 2x² +3y², and q(x+y)=4x-18y-39, where x and y are real numbers, what is the minimum value of p(x+y)-q(x+y)?
Click here to see answer by MathLover1(20850)

Question 1150766: if p(x+y) = 2x² +3y², and q(x+y)=4x-18y-39, where x and y are real numbers, what is the minimum value of p(x+y)-q(x+y)?
Click here to see answer by Edwin McCravy(20059)

Question 1151027: Given that y=-2/3x^3+5/2x^2-2/x,find the two values of x for which y is stationary. Show that the larger of these values of x corresponds to a minimum value of y.
Click here to see answer by Alan3354(69443)

Question 1151169: Find the equation of the tangent to that passes through the origin.
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Question 1151192: put the equation 16x^2+y^2+64x-2y+67=0 into conic standard form
Click here to see answer by Edwin McCravy(20059)

Question 1151192: put the equation 16x^2+y^2+64x-2y+67=0 into conic standard form
Click here to see answer by MathLover1(20850)

Question 1151192: put the equation 16x^2+y^2+64x-2y+67=0 into conic standard form
Click here to see answer by ikleyn(52798)

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