# Choose the correct option from the given alternatives: x2 + y2 = a2 is a solution of - Mathematics and Statistics

MCQ

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 = xsqrt(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 = a    ∴ 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
Is there an error in this question or solution?
Chapter 6: Differential Equations - Miscellaneous exercise 1 [Page 215]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 6 Differential Equations
Miscellaneous exercise 1 | Q 1.03 | Page 215
Share