Formula of centre of ellipse when the origin is shifted from (0,0)to some o
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Step-by-step explanation:
centre will be (x-a,y-b) where a,b is the new coordinate of origin
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The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is -
December 26, 2019
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Sunita Pradhan
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ANSWER
⇒ Distance between two foci=ae−(−ae)
=2ae=8 ………….(1)
⇒ Distance between two directrix=
e
a
−(
2
−a
)
=
e
2a
=18 ………..(2)
Multiply equation (1) & equation (2)
2ae⋅
e
2a
=8×18
4a
2
=144
a
2
=36
⇒a=6
From equation (1)
2ae=8
⇒e=
3
2
From the formula,
b
2
=a
2
(1−e
2
)
⇒6
2
(1−(
3
2
)
2
)
=36(1−
9
4
)
=36(
9
5
)=20
Equation of the ellipse is:-
a
2
x
2
+
b
2
y
2
=1
36
x
2
+
20
y
2
=1
⇒
100
5x
2
+9y
2
=1
⇒5x
2
+9y
2
=100
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