Question

(x-1)^2/9+(y+5)^2/16=1 what is major axis

Answer 1

16x^2 + 25y^2 + 32x - 150y - 159 =0
{(4X)^2+2*(4X)*4+4^2}-4^2+{(5Y)^2-2*(5Y)*15+15^2}-15^2-159=0
(4X+4)^2 + (5Y-15)^2 = 400
16(X+1)^2 + 25(Y-3)^2 =400...DIVIDING BY 400 THROUGHOUT..
(X+1)^2/25 + (Y-3)^2/16 =1
(X+1)^2/5^2 + (Y-3)^2/4^2 =1
COMPARING WITH ABOVE STANDARD EQN.
CENTRE IS (-1,3)
ECCENTRICITY E IS {(25-16)/25}^0.5=3/5
FOCI ARE (-1+5*3/5 ,3) AND (-1-5*3/5,3)=(2,3) AND (-4,-3)
MAJOR AXIS LENGTH = 2*5=10