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The differential equation of the family circles passing through the points (0, 2) and (0, 2) is:

Option 1 -

2 x y d y d x + ( x 2 − y 2 + 4 ) = 0

Option 2 -

2 x y d y d x + ( x 2 + y 2 − 4 ) = 0

Option 3 -

2 x y d y d x + ( y 2 − x 2 + 4 ) = 0

Option 4 -

2 x y d y d x − ( x 2 − y 2 + 4 ) = 0

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    2 months ago
    Correct Option - 1


    Detailed Solution:

    Equation of circle passing through (0, 2) and (0, 2) is

    x2+ (y2−4)+λx=0, (λ∈R)

    Divided by x we get

    x2+ (y2−4)x+λ=0

    Differentiating w.r.t. x

    x [2x+2y.dydx]− [x2+y2−4].1x2=0

    ⇒2xy.dydx+ (x2−y2+4)=0

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