Q. 495.0( 2 Votes )

The differential equation represents:
A. Family of hyperbolas

B. Family of parabolas

C. Family of ellipses

D. Family of circles

Answer :



y dy = (c – x)dx


Integrate


y dy = (c – x)dx


∫y dy = ∫(c – x)dx


∫y dy = ∫c dx – ∫x dx



k is the integration constant




x2 + y2 = 2cx + k


x2 + y2 – 2cx – k = 0


This is equation of circle because there is no ‘xy’ term and the coefficient of x2 and y2 is same.


This equation represents family of circles because for different values of c and k we will get different circles

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