SOLUTION: 9x^2 � 25y^2 + 150y � 450 = 0 Find the center, vertices, foci, and asymptotes of the hyperbola

Question 470747: 9x^2 � 25y^2 + 150y � 450 = 0
Find the center, vertices, foci, and asymptotes of the hyperbola
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
9x^2 � 25y^2 + 150y � 450 = 0
Find the center, vertices, foci, and asymptotes of the hyperbola
**
9x^2 � 25y^2 + 150y � 450 = 0
9x^2 � 25y^2 + 150y = 450
9x^2-25(y^2+6y+9)=450-225=225
9x^2-25(y+9)^2=225
x^2/25-(y+9)^2/9=1
This is a hyperbola with horizontal transverse axis, opens sideways.
Standard form: (x-h)^2/a^2-(y-k)^2/b^2=1
Center: (0,-9)
a^2=25
a=5
length of transverse axis=2a=10
vertices: (0�5,-9)
..
b^2=9
b=3
length of conjugate axis=2b=6
..
c^2=a^2+b^2=25+9=34
c=√34
Foci: (0�√34,-9)
..
Asymptotes:
slope, m=�b/a=�3/5
y= �mx+b
b=y-intercept=-9 (at center)
Equation of asymptotes:
y=�3x/5-9
see graph below as a visual check on answers.
..
y=�(9x^2/25-9)^.5-9

RELATED QUESTIONS
Find the center, the vertices, and the foci of the ellipse... (answered by lwsshak3)

How do you find the center, vertices, foci, and asymptotes of the hyperbola?... (answered by lwsshak3)

``Find the vertices,asymptotes, and the foci of the hyperbola.... (answered by ewatrrr)

Find the vertices, asymptotes, and foci of the hyperbola.... (answered by lwsshak3)

find the center, vertices, foci, and equations of the asymptotes whose equation is:... (answered by lynnlo)

I have to find the center, vertices, co-vertices, foci, and asymptotes of the hyperbola... (answered by lwsshak3)

Find the center, vertices, foci and asymptotes for the hyperbola x^2 - 9y^2 + 2x - 54y -... (answered by ikleyn)

Find the center, vertices, foci and asymptotes for the hyperbola 25x^2 - 4y^2 =... (answered by ikleyn)

find the center,transverse axis, vertices, foci and asymptotes of the hyperbola;... (answered by MathLover1)