The solution of `(dy)/(dx)=(a x+h)/(b y+k)` represent a parabola when (a) `( b ) (c) a=0,b!=0( d )` (e) (b) `( f ) (g) a!=0,b!=0( h )` (i) (c) `( d ) (e) b=0,a!=0( f )` (g) (d) `( h ) (i) a=0,b in R (j)` (k)

Options

A. `a=0, b ne 0`
B. `a ne 0, b ne 0`
C. `b=0, a ne 0`
D. `a=0, b in R`

Answer

A, C

Explanation

`(dy)/(dx) = (ax+h)(by+k)` or `(by+k)dy=(ax+h)dx`
or `by^(2)/2+y=a/2x^(2)+hx+C`
For this to represent a parabola, either `a=0, b ne 0` or `a ne0, b=0`