Question

2.
Find the eccentricity, coordinates of foci, length of latus
rectum and the equations of directrices of the ellipse
9x² + 16y2 - 36x + 32y - 92 = 0).​

Answer 1

Answer:

Ok didi i will answer after 10 minutes

Answer 2

ANSWER

We have 9x2 +16y 2−36x+32y−92=0

⇒9(x 2 −4x)+16(y 2 +2y)=92

⇒9(x2−4x+4)+16(y2+2y+1)=92+36+16=144

⇒9(x−2) 2 +16(y+1) 2=144

⇒ 16(x−2) 2 + 9(y+1) 2 =1

⇒a 2=16,b 2=9

Thus eccentricity, e= 1− a 2b 2 = 1− 169 = 4

and length of latus rectum = a2b 2 = 29

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