Question
Download Solution PDFThe sum of the focal distances of a point on an ellipse is constant and equal to the
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
From the figure and the property of ellipse
PM = (a/e) - x
And, SP = e × PM
⇒ SP = e × [(a/e) - x]
⇒ SP = a - ex ----(i)
Similarly from the figure and
PN = (a/e) + x
And, S'P = e × PN
⇒ S'P = e × [(a/e) + x]
⇒ S'P = a + ex ----(ii)
From equation (i) and (ii) we get
SP + S'P = a - ex + a + ex
⇒ SP + S'P = 2a (Length of major axis)
Important Points In the case of vertical ellipse it must be equal to the length of the minor axis.
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