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

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

Question 60702: I need to graph each function
y=x2-5x+6 (I tried to subscript the 2 but it didnt work)
f(x)=x2+4 (I tried to subscript the 2 but it didnt work)

Click here to see answer by funmath(2933)

Question 62309: need help on this one please
complete the square and write the given equation in the standard form for the equation of a circle. then give the center and redius of the circle and sketch a graph
x^2 + 8x + y^2 + 4y + 16= 0
Click here to see answer by funmath(2933)

Question 62576: How do I find the symmetry for y=-x^2+6x-9
Thanks for your help. Have a Happy thanksgiving.
Click here to see answer by funmath(2933)

Question 62719: please help
need the function listed below with it's graph.
f(x)= (x+2)^2
f(x)= -x^2+3
f(x)= x^2-2
f(x)= (x-2)^2
Click here to see answer by praseenakos@yahoo.com(507)

Question 62722: identify the graph of the function of y=f(x)= ^x+2
Click here to see answer by praseenakos@yahoo.com(507)

Question 62716: really need help
solve the system of nonlinear equations for x and y. sketch a graph of each equation showing the intersection points of the line and the parabola. x^2 + y=4 and 2x + y=1 thanks so much
Click here to see answer by ankor@dixie-net.com(22740)

Question 62721: please help
need the function listed below with it's graph.
f(x)= (x+2)^2
f(x)= -x^2+3
f(x)= x^2-2
f(x)= (x-2)^2
Click here to see answer by funmath(2933)

Question 62717: describe the graph of y^/25 - x^2/64 =1
Click here to see answer by rchill(405)

Question 63074: graph the parabola. find the vertex.
y=2(x+3)(x-1)
Click here to see answer by Edwin McCravy(20059)

Question 63653: Hello, I'm Alex. Could I please ask your assistance on these two Homeschool American School Problems because I don't have a teacher here to help?
(1) What is the equation of the perpendicular bisector of the line between points (2,2) and (6, 6)?
(2) What is the (a)directrix and the (b)focus of the parabola y = x^2 - 5x + 4?

Click here to see answer by venugopalramana(3286)

Question 63709: How do you Simplify the equations and graph: -4x^2+25y^2+16x-150+109=0
Click here to see answer by stanbon(75887)

Question 63780: y=-2x^2-16x-35
find the vertex
find the equation of the axis of symetry
find the coordinates of the focus
find the equation of the directrix
find the length of the latus rectum

Click here to see answer by venugopalramana(3286)

Question 63873: Please help me find the soultion of this word problem :
Erica has a difficult golf shot to make. Her ball is 120m from the hole. She wants the ball to land 10m in front of the hole, so it can roll to the hole. A 15m tree is two thirds the way between her ball and the hole.
a) Choose the base of the tree as the origin, write an algebraic equation to model the height of the ball to just clear the top of th tree, in 1) factored form 2) vertex form.
Click here to see answer by stanbon(75887)

Question 63939: y= 1/x
Click here to see answer by funmath(2933)

Question 64320: Find the equation of an ellipse with center at the origin, a vertical major axis of length 8, and a horizontal minor axis of length 4.
Could someone help please?
Click here to see answer by stanbon(75887)

Question 64314: I really don't understand these problems and need help.
State the location of the foci for this hyperbola:
(y-3)^2/11 - (x+1)^2/5 =1
Click here to see answer by venugopalramana(3286)

Question 64313: Which conic section is represented by this equation?
(x-2)^2=8y
Click here to see answer by venugopalramana(3286)

Question 64312: I just don't get these problems and need help please.
Which conic section is represented by this equation?
9x^2-36x-4y^2-24y-36=0
Click here to see answer by Earlsdon(6294)

Question 64382: please help me find the vertex, axis of symm., x and y intercepts, focus and directrix. It would be helpful if you could sketch the graphs showing the points.
y=-1/4(x-2)^2+4 and
x=3(y+1)^2-2
Thank you.
Click here to see answer by stanbon(75887)

Question 64380: Please help me use completing the sq. to write the equation in the form y=a(x-h)^2+k. Also identify the vertex, focus and directrix.
y=3x^2=12x=1.

Click here to see answer by stanbon(75887)

Question 64532: Is the conic section a curve formed by the intersection of two cones or just one? Or does it matter?
Click here to see answer by Earlsdon(6294)

Question 64530: Is the following equation an ellipse? I think it is but the 1 under the first part is making me question myself because it isn't "squared".
(x-3)^2/1 + (y+1)^2/25
Click here to see answer by Earlsdon(6294)

Question 64981: I am having trouble with hyperbolas. Please help me determine the foci and equations of the asymptotes of: 9x^2-25y^2=225. Thanks for your help.
Click here to see answer by funmath(2933)

Question 64838: Please tell me if I am on the right track. I am to sketch the graph and id the foci of: 9(x-1)^2+4(y+3)^2=36. I came up with foci (1,-3+sqrt5) and (1,-3-sqrt5). Which is (1,-.764) and (1,-5.236).
Then I am to find the center of x^2+y^2=12x-12y. I came up with the center at (6,-6)with radius sqrt72. How did I do?
Click here to see answer by funmath(2933)

Question 65049: I am having trouble using the point slope formula to find the equations of the asymptotes of ((x+3)^2/16)-((y+2)^2/25)=1. I know the slope is +or-5/4. I'm just not sure where to go from there. I also need some help finding the equation of the hyperbola described as having the foci at (5,0) and (0,-5) and the y-int. at (0,4) and (0,-4). Thank you very much.
Click here to see answer by cristiana(10)

Question 65149: The distance between the points (1,3) and (-2,7) is:
25 units
units
7 units
5 units
Each of the remaining questions refer to the parabola y = 2x 2 + 12x + 17
The vertex of the parabola is:
(3,1)
(3,-1)
(-1,3)
(-3, -1)
The focus of the parabola is:
(3, -9/8)
(-3, -9/8)
(-3, -7/8)
(3, -7/8)
The directrix of the parabola is:
The vertical line x = -9/8
The horizontal line y = -9/8
The horizontal line y = 9/8
The horizontal line y = -7/8
The length of the latus rectum of the parabola is:
17 units
1/8 unit
2 units
1/2 unit

Click here to see answer by stanbon(75887)

Question 65114: graph f(x)=xsquared-1
Click here to see answer by funmath(2933)

Question 65288: If the eccentricity of an ellipse (in other words, the value e) is close to zero, then the ellipse looks almost like a circle.
True
False
Each of the remaining questions refer to the ellipse 4x^ 2 + 9y ^2 - 8x + 36y + 4 = 0.
The center of the ellipse is at the point
(-1,2)
(-2,1)
(1,-2)
(2,-1)
The foci of the ellipse are the points
The length of the major axis of the ellipse is
6 units
3 units
4 units
2 units
The length of the minor axis is
3 units
6 units
4 units
2 units

Click here to see answer by Earlsdon(6294)

Question 65287: The graph of a circle describes y as a function of x.
True
False
Which of these equations describes a circle with radius 5 and center (3,-2) ? (x - 3) ^2 + (y + 2)^ 2 = 25
(x - 3) ^2 + (y + 2)^ 2 = 5
(x + 3) ^2 + (y - 2) ^2 = 25
(x + 3) ^2 - (y + 2) ^2 = 25

Which of these equations describes a circle with radius 3/2 and center (0,4) ? x^ 2 - (y - 4) 2 = 9/4
x^ 2 + (y - 4) 2 = 3/2
(x - 4) ^2 + y 2 = 9/4
x^ 2 + (y - 4) 2 = 9/4

The circle whose equation is x^ 2 + 2x + y ^2 + 6y + 6 = 0 h
as center (1,3) and radius 2
has center (-1, -3) and radius 2
has center (-1, -3) and radius 4
has center (1, 3) and radius 4
The circle whose equation is x^ 2 - 6x + y ^2 + 2y = -4

Click here to see answer by Edwin McCravy(20059)

Question 65443: (y*y)-2x-20y+94=0
Click here to see answer by Nate(3500)

Question 65743: A hyperbola is the only one of the conic sections whose graph contains two separate curves.
True
False
Each of the remaining questions refer to the hyperbola 36x 2 - 100y 2 - 72x + 400y = 3964.
The center of the hyperbola is
(2,1)
(1,2)
(-1,2)
(1,-2)
The foci of the hyperbola are at the points
(10.662, 2) and (-12.662, 2)
(-10.662, -2) and (12.662, -2)
(-10.662, 2) and (12.662, 2)
(2, -10.662) and (2, 12.662)
The length of the transverse axis is
5 units
10 units
20 units
none of the above

The equations of the two asymptotes are
y = (3/5)x + 7/5 and
y = (-3/5)x + 13/5

y = (-3/5)x + 7/5 and
y = (3/5)x + 13/5

y = (5/3)x + 7/5 and
y = (-5/3)x + 13/5

y = (3/5)x + 5/7 and
y = (-3/5)x + 5/13

Click here to see answer by venugopalramana(3286)

Question 64531: Could someone help, Locate the vertices of the following hyperbola:
(x-5)^2/81 - (y-7)^2/49 =1
Click here to see answer by venugopalramana(3286)

Question 66025: y2=2x
Click here to see answer by Edwin McCravy(20059)

Question 66204: the graph of y=f(x). graph each of the following
y=absolutevalue(f(x))
y=-f(x)
y=f(-x)
y=f(x+1)+1
Click here to see answer by Edwin McCravy(20059)

Question 66246: Please help sketch the graph and name the conic section with equation:
4x^2-16x+9y^2+18y=0 So far I have factored out the 4 and 9. What comes next?Thank you
Click here to see answer by checkley71(8403)

Question 66711: I have no idea how to do anything with conics, our teacher is not the best teacher and my question is, how to write an equation for the conic section- Ellipse with vertices at (-2,2) and (4,2) and co-vertices at (1,1) and (1,3)
Click here to see answer by Nate(3500)

Question 66491: How do I go about converting this equation to the standard form in order to graph the conic section? 4x^2-16x+9y^2+18y=0 I know I am supposed to complete the square...Thanks a bunch.
Click here to see answer by rapaljer(4671)

Question 64311: I do not understand these problems at all, could someone please help me?
The following equation represents an ellipse. True or False?
(x-3)^2/1 + (y+1)^2/25
Click here to see answer by rapaljer(4671)

Question 67368: Question 1 (10 points)
Find the distance between the two points (3,-4) and (-4,5)
Question 2 (10 points)
The idea of eccentricity is associated to which one of the four types of conic sections?
Question 3 (5 points)
Each of the next four questions refer to the parabola y = 5(x+2)^2 + 7.
Find the vertex of the parabola

Question 4 (5 points)
Find the focus of the parabola
Question 5 (5 points)
The directrix line of the parabola is the line y =
Question 6 (5 points)
The length of the latus rectum of this parabola is
Question 7 (20 points)
Find the standard form of the circle x^2 + y^2 + 2x - 6y - 6 = 0.
Question 8 (5 points)
For the circle x^2 + y^2 + 2x - 6y - 6 = 0 of the previous problem, find the center.
Question 9 (5 points)
For the same circle x^2 + y^2 + 2x - 6y - 6 = 0 of the previous two questions, find the radius.
Question 10 (20 points)
Find the standard form of the ellipse given by the equation x^2 + 25y^2 -2x + 150y + 201 = 0.
Question 11 (5 points)
Here is the equation of an ellipse in standard form: (1/16)(x + 2)^2 + (1/9)(y - 5)^2 = 1 . Each of the next four questions refer to this ellipse. Find the center of the ellipse.

Question 12 (5 points)
Find the foci of the ellipse.
Question 13 (5 points)
Find the length of the major axis.
Question 14 (5 points)
Find the distance between the two foci.
Question 15 (20 points)
Find the standard form of the hyperbola given by the equation 4x2 – 25y2 – 50y – 125 = 0.
Question 16 (5 points)
Here is the equation of a hyperbola in standard form: (1/10)(x - 1)^2 - (y - 1)2 = 1 . Each of the next four questions refer to this hyperbola. Find the center of the hyperbola.

Question 17 (5 points)
Find the foci of the hyperbola.
Question 18 (5 points)
One of the two axes (transverse or conjugate) is parallel to the y-axis. Find its length.
Question 19 (5 points)
Find the two asymptotes for the hyperbola

Click here to see answer by checkley71(8403)

Question 68506: How do you solve:
x^2+(y^2)/9=1
Click here to see answer by stanbon(75887)

Question 68518: I do not get how to do this problem. Please help
f(x) = (x+11)squared -6
Click here to see answer by Edwin McCravy(20059)

Question 68986: what is the standard form of the hyperbola ?
Click here to see answer by stanbon(75887)

Question 68611: I need to know how to solve this:
I need also:
Type of Conic__________
Standard Form__________
Center/Vertex__________
Direction __________
and How to Graph It
PLEASE help I have a test soon.
Click here to see answer by Nate(3500)

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