SOLUTION: Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes.
Vertices: (5,19),(5,-5)
Foci: (5,20),(5,-6)
Algebra.Com
Question 603022: Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes.
Vertices: (5,19),(5,-5)
Foci: (5,20),(5,-6)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes.
Vertices: (5,19),(5,-5)
Foci: (5,20),(5,-6)
**
Information given shows hyperbola has a vertical transverse axis:
Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1
..
For given hyperbola:
center: (5,7)
length of vertical transverse axis=24=2a
a=12
a^2=144
..
c=13
c^2=169
..
c^2=a^2+b^2
b^2=c^2-a^2=169-144=25
b=√25=5
..
asymptotes:
Asymptotes are straight lines which go thru center
Standard form: y=mx+b, m=slope, b=y-intercept
slope=±a/b=±12/5
..
y=12x/5+b
solving for b using coordinates of center
7=12*5/5+b
b=-12+7=5
y=12x/5-5
..
y=-12x/5+b
solving for b using coordinates of center
7=-12*5/5+b
b==12+7=19
y==12x/5+19
..
Equation of given hyperbola:
(y-7)^2/144-(x-5)^2/25=1
RELATED QUESTIONS
use the information provided to write the standard form equation of each hyperbola... (answered by stanbon)
Use the information provided to write the standard form equation of each hyperbola.... (answered by lwsshak3)
use the information provided to write the vertex form equation of each parabola.... (answered by lwsshak3)
Use the information provided to write the vertex form equation of each parabola.
Vertex... (answered by ewatrrr)
Use the information provided to write the vertex form equation of each parabola.
Vertex: (answered by josgarithmetic)
Given the hyperbola: 9x2 – 54x – 16y2 + 64y – 127 = 0
(answered by lwsshak3)
Use the information provided to write the standard form equation [(x^2/b^2)+ (y^2/a^2)=1] (answered by josgarithmetic)
Give the equation in standard form of the hyperbola with vertices (-4,2)
and (1,2) and... (answered by Edwin McCravy)
Write each equation in standard form and give the values of a,b and c
2y=8 (answered by solver91311)