A curve `C` passes through (2,0) and the slope at `(x , y)` as `((x+1)^2+(y-3))/(x+1)dot` Find the equation of the curve.

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as (x^2-2y)/x , then the curve also passes through the point

Find the asymptotes of the curve x y-3y-2x=0 .

A curve passing through the origin has its slope. e^(x) . Find the equation of the curve.

The slope of the tangent at (x , y) to a curve passing through a point (2,1) is (x^2+y^2)/(2x y) , then the equation of the curve is

Let C be a curve defined by y=e^a+b x^2dot The curve C passes through the point P(1,1) and the slope of the tangent at P is (-2)dot Then the value of 2a-3b is_____.

The slope of the tangent at (x , y) to a curve passing through (1,pi/4) is given by y/x-cos^2(y/x), then the equation of the curve is

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is

Find the equation of the curve passing through (1,0) and which has slope 1+(y)/(x) at (x,y)

A curve passes through the point (1,pi/6) . Let the slope of the curve at each point (x , y) be y/x+sec(y/x),x > 0. Then the equation of the curve is

The gradient (siope) of a curve at any point (x,y) is (x^(2)-4)/(x^(2)) . If the curve passes through the point (2 , 7) , then the equation of the curve is ,