The equation of the curve through the point (1,1) and whose slope is `(2ay)/(x(y-a))` is

Options

A. ` y^(a).x^(2a)=e^(y-1)`
B. ` y^(a).x^(2a)=e^(y)`
C. ` y^(2a).x^(a)=e^(y-1)`
D. ` y^(a).x^(a)=e^(y)`

Answer

a

Explanation

We have , slope `(dy)/(dx) = (2ay)/(x(y-a)) rArr (y-a)/y dy = (2a)/x dx`
On integrating both sides , we get
` y - a log |y| = 2a log | x| + log C`
` rArr y^(a) * x^(2a) = Ce^(y)`
This passes through (1,1) therefore 1 = Ce `rArr C = 1/e`
So , the equation of the curve is ` y^(a) * x^(2a) = e^(y-1)`