1.
25(y+6)2−39(x−4)2=1Center: (4,−6)
Vertices: (4,−11),(4,−1)
c2=a2+b2=25+39=64=>c=8 Foci: (4,−14),(4,2)
Endpoints of conjugate axis: (4−39,−6),(4+39,−6)
First asymptote: y=−39539(x−4)−6
Second asymptote: y=39539(x−4)−6
2.
9x2+126x−16y2−96y+153=0
9(x2+14x+49)−16(y2+6y+9)=144
16(x+7)2−9(y+3)2=1Center: (−7,−3)
Vertices: (−11,−3),(−3,−3)
c2=a2+b2=16+9=25=>c=5Foci: (−12,−3),(−2,−3)
Endpoints of conjugate axis: (−7,−6),(−7,0)
First asymptote: y=−43x−433
Second asymptote: y=43x+49
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