4. If the normal at one end of a latus rectum of the ellipse
=1 passes through one end of the minor axis,
b?
then show that et +e? = 1 (e = eccentricity of the
ellispe).
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1
Answer:
didi aapka koi test chal rha he kya
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ANSWER
Let a>b, then one of latus rectum of the ellipse is (ae, ab 2 )
Thus equation of normal at this point is given by,aea 2 x − b /ab 2 y =a2e2
Given it passes through one of minor axis ,which is (0,−b)
⇒ aea 2 (0) + b /ab 2 (−b) =a 2 e 2
⇒e 2 = ab
Now using e 2 =1− a 2b 2
we get, e 4 +e 2−1=0
which class u r
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