Precalc
posted by Grace .
A hyperbola has this Cartesian equation:
((x2)/5)^2 + ((y+1)/3)^2 = 1
A. Find direction in which it opens.
Horizontal?
B. Find the coordinates of the center.
I think it's (2,1) or (1,2)?
C. Find the slopes of the asymptotes: m=+ ?

change to more standard way of writing the hyperbola
(x2)^2 /25  (y+1)^2 /9 = 1
So the major axis is parallel to the yaxis and we have a vertical hyperbola
centre is ( 2,1) , (there is only one centre)
a = 5 , b = 3
I then sketch a rectangle that has (2,1) as its centre, having a height of 10 and a width of 6 , (2a and 2b)
So the coordinates of the main diagonal, which would be one of the asymptotes, are
(5,4) and (1,6)
Slope of that asymptote = (64)/(1,5) = 10/6 = 5/3
So the slope of the other one is 5/3
Quick way:
slope of asymptotes = ± a/b = ± 5/3
Respond to this Question
Similar Questions

math 30 conics
Hi i was given the equation (y2)^2  x^2/4 =1. I need to find the center, vertices and asymptotes of this hyperbola. I found the center (0,2) and the vertices were tricky but I think they are (0,1) (0,3) but I'm having trouble finding … 
Math
Find an equation for the hyperbola. vertices:(2,3)(2,3) Foci:(2,5)(2,5) I used the midpoint formula to find the center and I came up with (2,0). I just don't know how to find a and b. 
Precalc
Heres the equation: (x^2)(4y^2)(4x)+(24y)(36)=0 Your supposed to find the coordinates of the center, foci, and vertices, and the equations of the asymptotes of its graph. So first you complete the square right? 
math30
The equation of the hyperbola is (x3)^2/4  (y+1)^2/16 =1. What is the range? 
algebra
find an equation that models the path of a satelite if its path is a hyperbola, a=55,000km and c=81,000km assume that the center of the hyperbola is the origin and the tranverse axis is horizontal 
agebra
Can someone please help me.. find an equation that models the path of a satelite if its path is a hyperbola, a=55,000km and c=81,000km assume that the center of the hyperbola is the origin and the tranverse axis is horizontal 
Algebra
Tell whether the graph opens up or down. Find the coordinates of the vertex. Write an equation of the axis of symmetry. Y=3x^2 The graph opens up but I don't get how you would find the coordinates of vertex and how to write the equation … 
math
Let equation of an hyperbola be y^24x^2+4y+24x41=0 a. Find the standard form b. Find the center c. Find the vertices d. Find the foci e. Find the slant asymptotes 
chuka university
given the eccentilisty and a point that lies on the hyperbola ,find the equation of the hyperbola center origin 
Cartesian Equation
Determine the Cartesian equation of each of the following planes: b) through the points (3,0,1) and (o,1,1), and perpendicular to the plane with equation xyz+1=0 My teacher told me to find a direction vector, cross that with the …