Question

2. The differential equation of the family of the curves x2 + y2 - 2ax = 0 is
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Answer 1

Answer:y=-×+ax or xer or aer

Answer 2

$\huge{\boxed{\overline{\underline{\mathfrak{\fcolorbox{cyan}{blue}{Answer}}}}}}$

=> y² - x² = 2xyy'

The given equation is

x² + y² - 2ax = 0 .....(1)

On differentiating Eq. (1) with respect to x, we get

=> 2x + 2y dx/dy - 2a = 0

=> a = x + y dy/dx

On putting the value of a in Eq. (1), we get

x² + y² - 2x(x + y dy/dx) = 0

=> x² + y² - 2x² - 2xy dy/dx = 0

=> y² - x² - 2x² - 2xyy' = 0

(y'=dy/dx)

=> y² - x² = 2xyy'

silentlover45.❤️