Choose the correct option from the given alternatives:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of
Options
`("d"^2"y")/"dx"^2 + "yx" + ("dy"/"dx")^2 = 0`
`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
`"y" ("d"^2"y")/"dx"^2 + 2 ("dy"/"dx")^2 + "y" = 0`
`"xy" "dy"/"dx" + "y" ("d"^2"y")/"dx"^2 = 0`
Solution
`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
Hint:
`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` .....(1)
∴ `1/"a"^2 xx "2x" - 1/"b"^2 xx "2y" "dy"/"dx" = 0`
∴ `"x"/"a"^2 - "y"/"b"^2 "dy"/"dx" = 0` ....(2)
and `1/"a"^2 xx 1 - 1/"b"^2 ["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2] = 0` ....(3)
Equations (1), (2) and (3) are consistent
∴ `|("x"^2, - "y"^2, 1),("x", -"y" "dy"/"dx", 0),(1, -["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2], 0)| = 0`
∴ `"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`
