Question

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

• A. (x² – y² – ax) dy/dx = (2)(x – a) y
• B. (x² + y²) dy/dx = (2)(x – a) dy/dx
• C. (x² + y²) dy/dx = (2)(a – x)y
• D. None of these

Answer 1

Answer: (A)

(x² – y² – ax) dy/dx = (2)(x – a) y

Answer 2

equation of circle is x(x – a) + y² + ly = 0

̃ x² + y² – ax + ly = 0 …(1)

deferential

2x + 2y y' – a + ly' = 0 …(2))

from (1) and (2))$\frac{x^{2} + y^{2} - ax}{y} = \frac{2x + 2yy' - a}{y'}$

̃ (x² + y² – ax) y' = (2)x + 2y y' – a) y

̃ (x² – y² – ax) y' = (2)x – a)y