The tangent at any point `(x,)` of a curve makes an angle `tan^-1(2x + 3y)` with x-axis. Find equation of the curve if it passes through `(1,2).`

The tangent at any point (x , y) of a curve makes an angle tan^(-1)(2x+3y) with x-axis. Find the equation of the curve if it passes through (1,2).

The tangent at any point (x,y) of a curve makes an angle tan -1(2x+3y) with x-axis. Find the equation of the curve if it passes through (1,2).

If the tangent at any point on the curve y=x^(5)+5x-12 makes an angle theta with the x - axis then theta is

If slope of the tangent at the point (x, y) on the curve is (y-1)/(x^(2)+x) , then the equation of the curve passing through M(1, 0) is :

If slope of the tangent at the point (x, y) on the curve is (y-1)/(x^(2)+x) , then the equation of the curve passing through M(1, 0) is :

A curve y=f(x) passes through the 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. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P .

The slope of the tangent to the curve at any point is equal to y + 2x. Find the equation of the curve passing through the origin .

The slope of the tangent to the curve at any point is equal to y + 2x. Find the equation of the curve passing through the origin .