Question

27. Find the eccentricity, length of latus rectum, foci and the equations of directrices of the ellipse
25x2 +972 - 50x - 36y - 164 = 0.
28
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Answer 1

Answer:

We have 9x

2

+16y

2

−36x+32y−92=0

⇒9(x

2

−4x)+16(y

2

+2y)=92

⇒9(x

2

−4x+4)+16(y

2

+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

2

b

2

=

1−

16

9

=

4

7

and length of latus rectum =

a

2b

2

=

2

9