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

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Question 69425: i have to write the circle in standard form. then give the centeer and radius of the circle. x^2+y^2+8x-2y-8=0
Click here to see answer by funmath(2933)

Question 69661: does this equation describe an ellipse? 5y^2-18x+7=20y+3x^2-16
this is what I did
-3(x^2+6x+9) + 5(y^2-4y+4)=-23+20+(-27)
-3(x+3)^2/-30 + 5(y-2)^2/-30=-30/-30
(x+3)^2/-10 + (y-2)^2/-6=1
Click here to see answer by stanbon(75887)

Question 70091: Find the center,foci,and vertices of the ellipse and determine the lenghts of the major and minor axis. Then sketch the graph.
(x+2)^2/4+y^2=1 I thought both numbers in the equation needed a denominator. I put a 1 under the y^2. Is this correct?
The center: (2,0)
a^2=4 so a=+or-2
Vertices: (-2,0+or-2)-->(-2,2),(-2,-2)
Major Axis: 2a=2*2=4
Minor Axis: 2b=1
b^2=1-->b=+or-1
Foci: (-4,0) (0,0)
Is this correct? I don't have a problem with the sketching. I just do not understand how to do it without the denominator under y^2.
Click here to see answer by stanbon(75887)

Question 70324: My son is in 10th grade, taking Algebra II. They just started this new section last week when my son was out sick two days. He is struggling with understanding his make-up work and won't be able to see the teacher until Tuesday after school. I hope you can help me help him in the meantime?
I'm not sure how to symbolize square root in your system either?
I'll use "sq rt" for square root -- ok?
Here is what he's done so so far, squaring, simplifying and getting the GCF
(5 times sq rt of 3 + 3 times sq rt of 5)(squared)
work:
(25x9) + 30 times sq rt of 15 + (9x5)
answer:
270 + 30 times sq rt of 15
Is that anywhere near correct?
Thank you so much!
Click here to see answer by stanbon(75887)

Question 70615: ah help meeeeeee :[[ it says determine whether each parabola opens upward,downward,left or right.

1) y=-6x[squared]
2) 2x+6y[squared]=0
THEN, it says identify the focus and the directix of the graph of each equation
:(
y=-8x[squared]
x-5y[squared]0
thanks guys :(
Click here to see answer by stanbon(75887)

Question 70893: AH peoplle please help im stuck on these!!
ahh
:(

it says Determine an equation of the parabola with the following property
1) Focus at (0,-6) and directrix y=6.

THEN it says
determine the vertex,focus,and directrix for each parabola. Sketch each parabola.
1) y[squared]=-3x
2)x[squared]=12y
3) x[squared]-8x-y+20=0

oh man please help anyone! :(
Click here to see answer by stanbon(75887)

Question 71320: For each point in a set of points, its distance from (3,4) is four times its distance from (-5,2). Find the equation and determine what conic section the graph will be.
Click here to see answer by sudhir(14)

Question 71710: can you help me understand this problem
find an equation of the circle with center (7, -2) and radius square root of 5

Click here to see answer by funmath(2933)

Question 71804: after i find the focus,directrix, aixis of symmetry, vertex and everything else how do i graph the parabola?
Click here to see answer by Edwin McCravy(20058)

Question 72354: Find theexact solution(s)of each system of equations.
y^2=x^2-7
x^2+y^2=25
Click here to see answer by pradhyumna.kumar@gmail.com(62)

Question 72735: I keep finding examples that have the problem squared but none without. I would appreciate any and all help with this.
Find the vertex of y=-2(x -3) + 4 and then graph.
I think the vertex is (6,4) and the -2 makes it open downward if im correct. I came up with (5,0) and (-1,0) as the x intercepts and (0,10) as the y intercept. When I plot them on a graph with the vertex, the points are all over the graph so Im doing something wrong. Please please help!
Click here to see answer by stanbon(75887)

Question 72742: What is the equation of the parabola: Vertex at (2,-3): focus at (2, -5)? I really don't understand where in the equation the focus and vertex would be placed. Thank you.
Click here to see answer by stanbon(75887)

Question 73824: ELLIPSE WITH CENTER (0,2);HORIZONTAL MAJOR AXIS OF 6;MINOR AXIS OF 4
Click here to see answer by stanbon(75887)

Question 74051: please help explain this equation:
find the vertex, focus, axis, directrix and latus rectum of the parabola
x^2+y=6x-14.
i found the vertex to = (3, -5)
i am not sure how to find the rest..thanks for any help.
this is from a problem we were given in class
Click here to see answer by checkley75(3666)

Question 74046: can you help me with question?
this is from a hand out.
Find the center and radius of x^2+y^2-x+2y-3=0
I figured r=square root 17/2
and c=(0.5,-1)

Click here to see answer by jim_thompson5910(35256)

Question 74198: Can you please help me solve: A parking lot is to be formed by fencing in a rectangular plot of land except for an entrance 12 m wide along one of the sides. Find the demensions of the lot of greatest area if 300 m of fencing is to be used.
Click here to see answer by checkley75(3666)

Question 74196: Can you please help me solve: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons per day. The manager estimates that the company will lose 15 passengers for each increase of $1 in the fare. Find the fare that yields the greatest income.
Click here to see answer by stanbon(75887)

Question 74290: Find the center, vertices and foci of the following ellipse:
(x + 3)^2/9 + (y + 1)^2/16 =1
Click here to see answer by funmath(2933)

Question 74502: please help me find the vertex, focus and directrix of the parabola if the question is:
(x - 1) + 8(y + 2)^2 = 0
Click here to see answer by stanbon(75887)

Question 74533: Hi! I just submitted this problem, but I think I figured it out! Can someone tell me if this is correct?
Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).

The length of the major axis would be 12 units. 2a=12. a=6.
The length of the minor axis is 8 units. 2b=8. b=4.
The equation for an ellipse is y^2/a^2 + x^2/b^2=1.
So the answer would be y^2/36 + x^2/16=1.
Can someone please tell me if I did this right?
Click here to see answer by stanbon(75887)

Question 74529: Hi! Can someone please help me with this problem?
Write an equation for an ellipse if the points of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).

Thanks!
Click here to see answer by funmath(2933)

Question 74446: Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).
My book doesn't show me how to write the equation with the major and minor axis points. Can someone help me? Thanks!
Click here to see answer by scott8148(6628)

Question 74598: anybody good at parabolas?
on my "Y" axis from 1 through 5 the top of the parbola (known as V(-3,4)) is at 4 where it begins its downward peak.
on the "X" axis the right leg comes through -1 curves through the "Y" axis of 4 and the left leg goes back down through -5 on the "x" axis.
Question: Determine the standard equation of the parabola.
I know you people are whizzes and I would really be impressed. I have missed every question concering parabolas.
Thank you
Click here to see answer by stanbon(75887)

Question 74582: Find an equation of the circle of radius 4 that is tangent to both branches of the graph y=|x|
Click here to see answer by scott8148(6628)

Question 74663: i need some help with question..
the equation of the asymptotes of the hyperbola x^2/a^2-y^2/b^2=1 are______?
thanks
Click here to see answer by jim_thompson5910(35256)

Question 74667: i am having trouble understanding these types of questions..can you help?
length of the major axis of the ellipse 3x^2+2y^2=6 is __________?
this is a problem we had in our class to be reviewed tomorrow..thanks.
Click here to see answer by stanbon(75887)

Question 74668: we are doing these types of questions in class. i am having a problem understanding how to solve.can you help?
the foci of the ellipse x^2/a^2+y^2/b^2=1b>a are_______
thanks for any insight into this..
Click here to see answer by josmiceli(19441)

Question 74666: could someone help me with this problem?
the focus of the parabola 4y^2+12x-12y+39=0 is________?
how do i find this? thanks for your help..it was a problem presented in class.
Click here to see answer by stanbon(75887)

Question 74682: sketch a graph of the following (find and include focal points, verticies, asymptotes, directrix, as appropriate). Estimate any irrational values on the graph.
1. y = 2x^2 - 10x + 27
first i tried to get all of the x and y's to one side, then complete the square, but i didn't know how because y in this problem is not squared...but i tried it anyway and got... 27/4 (y-27)= x^2 - 5x + 25/4 ...i'm not sure where to go from here>???
Click here to see answer by stanbon(75887)

Question 73350: The pool at a park is circular. You want to find the equation of the circle that is the boundary at the pool. Find the equation if the area of the pool is 900 square feet and (0,0) represents the center of the pool. Use EXACT values only.
I thought my answer was right, but it's not; what did I do wrong + what is the correct answer?
x^2 + y^2 = 286.4788976
Click here to see answer by jim_thompson5910(35256)

Question 74665: i could use some help understanding this question.
in the equation of the hyperbola x^2-y^2=9, e=_____
thanks for your help
Click here to see answer by venugopalramana(3286)

Question 74846: i am working on hyperbola's and im not sure if i am understanding it yet. could see if i got the right answer to this one? thanks for any help. this is from a problem we had in class.
The center of the hyperbola 9x^2-16y^2-18x+32y-151=0
the answer i got was (1,1)
Click here to see answer by Nate(3500)

Question 74847: could you help me with this equation? it is from a question we had in class.
The focus of (x-1)^2 = (y-2) is_____.
i said the answer is (-2,-1)
can you tell me if i got it right? thanks for any help.
Click here to see answer by Nate(3500)

Question 74845: i am working on hyperbola's and im not sure if i am understanding it yet. could see if i got the right answer to this one? thanks for any help. this is from a problem we had in class.
The center of the hyperbola 9x^2-16y^2-18x+32y-151=0
the answer i got was (1,1)
Click here to see answer by venugopalramana(3286)

Question 67664: how would you solve y=1/9000x2+5 and y=1/9000(x-2100)^2+5 and how to graph?
Click here to see answer by Nate(3500)

Question 75003: parabola with vertex at (-3,1) and directrix x=-8
Click here to see answer by stanbon(75887)

Question 75566: Can you please help me?
1. Write the equation of an ellipse with center (8, 7), horizontal major axis length 16, and minor axis length 4.

2. Write the equation of an ellipse with center (9, �3), horizontal major axis length 18, and minor axis length 10.
Thankyou

Click here to see answer by chitra(359)

Question 75551: will u please help me answer these questions i am having a test on it on Next Tuesday march 27,2007
Click here to see answer by chitra(359)

Question 75528: I am graphing parabolas and I have a quick question...
How would I graph x=(1/24)(y^2)?
I know that the vertex is (0,0), the focus is (6,0) and the directrix is x=-6
Thank you
Click here to see answer by stanbon(75887)

Question 75629: I understand the definition of a hyperbola. However, I am having a problem understanding what is being asked in the question below. What�s the best way to answer it? Any help is greatly appreciated.
Regarding a hyperbola, what happens to y as x gets larger? In addition, what happens to x as y gets larger?

Click here to see answer by jim_thompson5910(35256)

Question 76154: Hello, I've struggled with conic sections for two months and keep getting the wrong answers. I skipped #s 3 and 4 on circles because those were right.

Problem #5: "Find the foci for the ellipse and sketch a graph of
."

Unfortunately, all I got was a foci at +4,0 and -4,0; but I don't know how to graph it.
Click here to see answer by checkley75(3666)

Question 76299: Please help me!!
directions: Identify the conic section represented by the eqation by writing the equation in standard form.
(-x^2) + (y^2) + (4y) - (16) = 0

thank you
Click here to see answer by stanbon(75887)

Question 76855: write in standard form
an ellipse with major axis 6 units long and parallel to the x-axis minor axis 4 units long, and center at (8,6)
Click here to see answer by Edwin McCravy(20058)

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