The equations of latusrecta of the hyperbola  5x2−4y2−30x−8y−39=0  are

Write in standard form x=h±ae 5(x2−6x)−4(y2+2y)=39 5(x2−6x+9)−4(y2+2y+1)=45−4+39=41+39=80 ⇒(x−3)216−(y+1)220=1  ⇒(h,k)=(3,−1) a2=16,b2=20 e=a2+b2a=364=64=32 x=3±4(32)=3±6⇒x=9,−3 ⇒x=9,x=−3