If a x²+2 h x y+b y²+2 g x+2 f y+c=0 represents a joint equation of directrices of the hyperbola 16 x²-9 y²=144 , then g+f-c=

Step-by-step solution

Equation of the hyperbola: 16 x²-9 y²=-144 This can be rewritten in the following way: x² 9 - y² 16 =-1 This is the standard equation of a hyperbola, where array l a²=9 and b²=16 a²=b² (e²-1 ) 9=16 (e²-1 ) e²-1= 9 16 e²= 25 16 e= 5 4 array Coordinates of foci are given by (0, a e) , i.e. (0, 5) . Equation of the directrices: y= a e y= 4 5 4 5 y 16=0 Length of the latus rectum of the hyperbola = 2 a² b Length of the latus rectum = 2 9 4 = 9 2 .