SOLUTION: Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph {{{y^2-x^2+2x-6y+7=0}}}

Question 603270: Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Identify the conic section, re-write the equation in standard form, list the main characteristics, and graph
y^2-x^2+2x-6y+7=0
complete the squares
(y^2-6y+9)-(x^2-2x+1)=-7+9-1
(y-3)^2-(x-1)^2=2
(y-3)^2/2-(x-1)^2/2=1
This is a hyperbola with vertical transverse axis.
Its standard form of equation: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola:
equation: (y-3)^2/2-(x-1)^2/2=1
Center: (1,3)
a^2=2
a=√2
length of vertical transverse axis=2a=2√2
b^2=2
b=√2
c^2=a^2+b^2=2+2=4
c=√4=2
Foci: (1, 3�c)=(1, 3�2)=(1, 1) and (1,5)

RELATED QUESTIONS
Classify the conic section, write it's equation in standard form, and graph.... (answered by ewatrrr)

write in equation in vertex form and identify the conic section and graph it.... (answered by stanbon)

Identify the conic section represented by the equation: y^2 + 2y + 1 = 6x - x^2. Write in (answered by vleith,solver91311)

Identify the conic section, write each in standard form, and graph:... (answered by stanbon)

Identify the conic section and write the standard form of the equation... (answered by scott8148)

Classify the conic section and write its equation in standard form.... (answered by stanbon)

classify the conic section defined by thr equation. write the standard equation of the... (answered by jim_thompson5910)

write an equation of the conic section parabola with vertex at (2,6) and directrix at... (answered by lwsshak3)