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MCQ

**Choose the correct option from the given alternatives:**

x^{2} + y^{2} = a^{2} 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"`

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#### Solution

y = x`"dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`

**Hint:**

x^{2} + y^{2} = a^{2 } ∴ 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"`

Concept: Formation of Differential Equations

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