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Question
Find the differential equation of the ellipse whose major axis is twice its minor axis.
Solution
Let 2a and 2b be lengths of major axis and minor axis of the ellipse.
Then 2a = 2(2b)
∴ a = 2b
∴ equation of the ellipse is
`"x"^2/"a"^2 + "y"^2/"b"^2 = 1`
i.e. `"x"^2/(2"b")^2 + "y"^2/"b"^2 = 1`
∴ `"x"^2/(4"b"^2) + "y"^2/"b"^2 = 1`
∴ x2 + 4y2 = 4b2
Differentiating w.r.t. x, we get
`"2x" + 4 xx "2y" "dy"/"dx" = 0`
∴ `"x" + "4y" "dy"/"dx" = 0`
This is the required D.E.
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