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

Tutors Answer Your Questions about Quadratic-relations-and-conic-sections (FREE)

Question 269783: How do I write the equation of the ellipse in standard form? Thank-you!
Click here to see answer by drk(1908)

Question 270001: I'm not sure how to solve quadratic systems. Here is an example of a problem:

x-y=1
Click here to see answer by stanbon(57347)

Question 270989: y=.5xsquared - 6x + 12
I need to get it into the equation of (x-x1) quantity squared + (y-y1) quantity squared= a whole number. Once in that form, I know how to graph.
Click here to see answer by josmiceli(9678)

Question 271750: The B Bridge connects SI and NY to NJ. It has an arch in the sharpe of a parabola that opens downward. Write an equation of a parabola to model the arch, assuming that the origin is at the surface of the water, beneath the vertex of the arch. end to end bridge if 1675 ft; base to top is 325 ft.
This is in chapter 8, pg 424 problem 43 of Glencoe Mathematics, algebra 2
Click here to see answer by ankor@dixie-net.com(15652)

Question 272425: please help
Parabola: y=x^2+6x+5 , give vertex & x & y axis
Click here to see answer by oberobic(2304)

Question 272925: Hyperbola
4x^2-y^2=16
Please help!
Click here to see answer by richwmiller(9135)

Question 273332: My Textbook gives a sample hyperbola equation
(x^2 / 9) - (y^2 / 16) = 1
It then has
y = ±(4/3)√x^2 - 9
I would like someone to explain to me step by step how my textbook got to this answer or is it that i am missing out on some detail.
Click here to see answer by stanbon(57347)

Question 273593: Molly's Custom Kitchen Supplies sells handmade forks and spoons. It cost the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?
Click here to see answer by Theo(3464)

Question 274145: Some nuclear power plants utilize "natural draft" cooling towers in the shape of a hyperboloid, a solid obtained by rotating a hyperbola about its conjugate axis. Suppose such a cooling tower has a base diameter of 400 feet, and the diameter at its narrowest point, 360 feet above the round, is 200 feet. If the diameter at the top of the tower is 300 feet, how tall is the tower?
Click here to see answer by CharlesG2(828)

Question 274415: Find x and y:
x+y=7 and x*y=11
Click here to see answer by stanbon(57347)

Question 274983: what is the multiplicative identity of 21m3n5
Click here to see answer by user_dude2008(1861)

Question 275418: Hello :)
Can you please help me with this homework, it says,
1) create a design that you want to make using only parabolas and circles. Each design must include at least one parabola and one circle.
2) must have at least 4 conics in the design and write the equation for each conic.
I was thinking of a smile shape, but I wasn't sure its the write design for the teacher rules and how to get the equation for a smile.
I appreciate your help in advance!
Thank you,
Tena
Click here to see answer by stanbon(57347)

Question 275556: m-1/4sq
Click here to see answer by Alan3354(30993)

Question 275673: About a hyperbola. When you havean an equation like x^2/49-y^2/169=1... How do I make it so it's not huge on the paper? For example.. I am making a picture with different equations. I am making a cross in particular.
Click here to see answer by Alan3354(30993)

Question 275652: PLEASE HELP?? Thank you SO MUCH!!!
Write the equation that best represents an ellipse that has a vertex at (–4, 0), a co-vertex at (0, 1), and is centered at the origin.

Click here to see answer by richwmiller(9135)

Question 276019: How do I determine if a parabola has real or complex roots?
Click here to see answer by stanbon(57347)

Question 276514: Which of the following circles have their centers on the y-axis? Check all that apply.
A. (x - 0)2 + (y + 5)2 = 74
B. (x + 1)2 + (y - 7)2 = 16
C. (x - 4)2 + (y - 0)2 = 22
D. (x - 0)2 + (y - 0)2 = 44

Click here to see answer by Alan3354(30993)

Question 276774: Find the exact solution of y=x+2
y=x^2
Click here to see answer by checkley77(12569)

Question 277525: If a right circular cone intersects a plane that passes through one of its nappes, but the plane is neither parallel to the edge of the cone nor perpendicular to the cone's axis, the resulting curve will be a(n) _____.

Click here to see answer by Alan3354(30993)

Question 277474: X^2-4x+8y+28=0 . Is this a hyperbola, ellispes or parabola
Click here to see answer by scott8148(6628)

Question 277762: I need help on this new form of equation that we're learning in school that I still don't understand. It evidently has something to do with parabolas. Here's the problem:
In firefighting, a good water stream can be modeled by:
y=-0.003x^2 + 0.62x + 3
where x is the water's horizontal distance traveled (in feet) and y is its corresponding height (in feet). If a firefighter is aiming a good water stream at a building's window 25 feet above the ground, at what two distances can the firefighter stand from the building?
Please help me. I have no idea where to even start.
Click here to see answer by richwmiller(9135)

Question 278068: i'm learning about ellipses and i have the problem:
x squared+4y squared-6x+24y+41=0
i need to find the center, foci, and vertices.
i have no idea how to even start, i tried by first completing the square but i'm missing something because i get confused by that 41 that is thrown in there, please help.
Click here to see answer by Edwin McCravy(8909)

Question 278289: What is the vertex of X= 1(over)3 -2y-9
Click here to see answer by stanbon(57347)

Question 278971: I need to write the vertex form equation of the parabola with the given information:
Opens up or down, Vertex (-10,3), passes through (-8,7)
Can someone help me throught this step by step please?
Click here to see answer by Edwin McCravy(8909)

Question 279569: Can you please help me? here's the equation:

the teacher gave us answer and the answer is supposedly:
1 over x-5
i don't understand where the 1 comes from and where the x+5 goes.
so far I've factored the bottom out but thats as far as i can get and he didnt explain.
Click here to see answer by richwmiller(9135)

Question 279767: find the equation, in standard form, of the parabola

Click here to see answer by Edwin McCravy(8909)

Question 279666: if the parabola y-2=a(x-3)^2 goes through point 2,0 what is the value of a. i think the answer is a=-2 is that correct
Click here to see answer by richwmiller(9135)

Question 279925: Find the equation of the ellipse with center (–5, –2), horizontal major axis of length 6, and minor axis of length 4.
Click here to see answer by stanbon(57347)

Question 280228: For each quadratic function (a) find the vertex and the axis of symmetry and (b) graph the function.
g(x)=x^2+5x+4.
a=1, b=5 and c=4
I started doing the problem and here is what I have so far.
x = -b/2*a
x= -5/2*1 = -5/2 or -2.5
g(1)= 1*(1)^2 + 5(1) + 4
g(1)=1 + 5 +4
So the vertex is (-2.5, 10).
Now I am confuse on how to get the axis of symmetry.
g(1)= 10
Click here to see answer by stanbon(57347)

Question 280545: Graph the following conic sections. Be sure to label your graph.

Click here to see answer by richwmiller(9135)

Question 280601: find vertex of the parabola y=4x squared - 16x - 11
Click here to see answer by richwmiller(9135)

Question 280514: write an equation for the ellipse with end points of the major axis at (7,1) and (-7,1) and end points of the minor axis at (0,5) and (0,-3). plz explain step by step...thnx
Click here to see answer by jsmallt9(3296)

Question 281139: I have to find the vertex, focus, which way it opens, the directrix, axis of symmetry, the length of LR, and the endpoints of LR. The equation is: (x+3)^2=10(y-4). So far I have tried and found the vertex is: (-3,4) and the focus is: (-3,2.5), it opens up, the directrix is y=-2.5, and the axis of symmetry is x=-3. But when I tried to graph it it didn't work out. Can you help me?
Thank you.
Click here to see answer by richwmiller(9135)

Question 281218: Suppose you are offered two jobs. One pays $30,000 the first year with annual raises of $2000 each year. The second offers a starting salary of $27,000 and raises of 8% each year. At the end of ten years, what would your yearly salary be from the first job and the second job?
Click here to see answer by richwmiller(9135)

Question 281302: 2x^2+y^2-12x-16y+10=0
how do i convert this to standard form of a conic section
Click here to see answer by richwmiller(9135)

Question 281498: Could you please show me how to do the following question because I got it wrong. The circle x^2 + y^2 - 2x - 3 =0 is stretched horizontally by a factor of 2 to obtain an ellispe. What is the equation of this ellipse in general form.Please help and thank you for your time.
Click here to see answer by CharlesG2(828)

Question 281466: state which type of conic section each equation represents. then put the equation into standard form.
x^2+9y^2-4x+54y+49=0
Click here to see answer by Mathematicians(84)

Question 281727: find the center of a circle with equation x^2+y^2-6x+4y-4=0
Click here to see answer by Greenfinch(383)

Question 281712: find the center and the radius of the circle
x^2+y^2-10x-6y+29=0.

Click here to see answer by richwmiller(9135)

Question 281728: find the length of the major axis of the ellipse with equation 4(x+4)^2+9(y-1)^2=36
Click here to see answer by Edwin McCravy(8909)

Question 281731: what are the slopes of the asymptotes of the hyperbola with equation

Click here to see answer by Edwin McCravy(8909)

Question 281903: Find the center, vertices, foci, and asymtotes of the hyperbola
4x^2-y^2-8x+2Y-1=0 AND GRAPH
Find the vertex, fous, and directrix of the parabola x^2-4x-4y+16=0 GRAPH
Click here to see answer by Edwin McCravy(8909)

Question 282004: what type of conic does this represent (x-3)^2/9 + (y-2)^2/4=1. i think its a hyperbola but im not sure
Click here to see answer by Alan3354(30993)

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