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Expert Question:
Ellipse
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Analytical Geometry
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Author
Message
3 Jul 2007 00:54:43 IST
Subject:
Ellipse
mohit kumar
(
5
)
1
[
1
rates]
total posts:
8
Offline
If the chord through the points whose eccentric angles are
&
on the ellipse, x
2
/a
2
+ y
2
/b
2
= 1 passes through the focus, then the value of tan(
/2) tan(
/2) is:
(A) e+1/e-1 (B) e-1/e+1 (C) 1+e/1-e (D) 1-e/1+e
3 Jul 2007 10:13:46 IST
Subject:
Re:Ellipse
Accepted Answer
[?]
geethu
(
711
)
121
[
174
rates]
total posts:
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given pts r (acos
, bsin
) & (acos
, bsin
);
line througth them is (y-bsin
) / (x-acos
) = (bsin
-bsin
) / (acos
-acos
)
it passes through focus (ae,0)
so,(0-bsin
) / (ae-acos
) = (bsin
-bsin
) / (acos
-acos
)
-sin
/ (e-cos
) = 2cos(
+
/2)sin(
-
/2) / 2 sin(
+
/2)sin(
-
/2)
tan(
+
/2) = (e-cos
)/sin
let tan
/2 =x & tan
/2 =y
so (x+y)/(1-xy) = [e - (1-x
2
)/(1+x
2
)] / [2x/(1+x
2
)] = [(1+x
2
)e +x
2
-1] / 2x
(1+x
2
)e = 2x(x+y)/(1-xy) + (1-x
2
) = (x
2
+xy+1+x
3
y)/(1-xy) = (1+xy)(1+x
2
)/(1-xy)
ie e=(1+xy)/(1-xy) ie tan
/2tan
/2 = xy = (e-1)/(e+1)
KINDLY RATE ME 4 MY EFFORTS PLZZZZZZZZZ.........
this reply: 17
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1
& 
on the ellipse, x2/a2 + y2/b2 = 1 passes through the focus, then the value of tan( 
