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Question
Choose the correct option from the given alternatives:
x2 + y2 = a2 is a solution of
Options
`("d"^2"y")/"dx"^2 + "dy"/"dx" - "y" = 0`
y = x`sqrt(1 + ("dy"/"dx")^2) + "a"^2 "y"`
y = x`"dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`
`("d"^2"y")/"dx"^2 = ("x + 1")"dy"/"dx"`
Solution
y = x`"dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`
Hint:
x2 + y2 = a2 ∴ 2x + 2y`"dy"/"dx" = 0`
∴ `"dy"/"dx" = - "x"/"y"`
∴ `"x" "dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`
`= "x"(- "x"/"y") + "a"sqrt(1 + "x"^2/"y"^2) = - "x"^2/"y" + "a" xx "a"/"y"`
`= ("a"^2 - "x"^2)/"y" = "y"^2/"y" = "y"`
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