Posted by Grace on Friday, January 20, 2012 at 12:39am.
A hyperbola has this Cartesian equation:
-((x-2)/5)^2 + ((y+1)/3)^2 = 1
A. Find direction in which it opens.
B. Find the coordinates of the center.
I think it's (-2,1) or (1,-2)?
C. Find the slopes of the asymptotes: m=+- ?
- Precalc - Reiny, Friday, January 20, 2012 at 9:32am
change to more standard way of writing the hyperbola
(x-2)^2 /25 - (y+1)^2 /9 = -1
So the major axis is parallel to the y-axis 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 = (-6-4)/(-1,-5) = -10/-6 = 5/3
So the slope of the other one is -5/3
slope of asymptotes = ± a/b = ± 5/3
Answer This Question
More Related Questions
- math30 - The equation of the hyperbola is (x-3)^2/4 - (y+1)^2/16 =-1. What is ...
- Pre-calc - Heres the equation: (x^2)-(4y^2)-(4x)+(24y)-(36)=0 Your supposed to ...
- math - Let equation of an hyperbola be y^2-4x^2+4y+24x-41=0 a. Find the standard...
- algebra - find an equation that models the path of a satelite if its path is a ...
- agebra - Can someone please help me.. find an equation that models the path of a...
- math 30 conics - Hi i was given the equation (y-2)^2 - x^2/4 =1. I need to find ...
- chuka university - given the eccentilisty and a point that lies on the hyperbola...
- Math - Find an equation for the hyperbola. vertices:(2,3)(2,-3) Foci:(2,5)(2,-5...
- Algebra - Tell whether the graph opens up or down. Find the coordinates of the ...
- Precalc - An ellipse has this Cartesian equation: ((x-2)/5)^2 + ((y-4)/3)^2 = 1 ...