If the tangent to a curve at a point `(x ,\ y)` is equally inclined to the coordinate axes, then write the value of `(dy)/(dx)` .

If a line is equally inclined with the coordinate axes, then its direction cosines are

Write the direction cosines of a line equally inclined to be three coordinate axes.

If the tangent line at a point (x ,\ y) on the curve y=f(x) is parallel to x-axis, then write the value of (dy)/(dx) .

If the bisector of angle A P B , where P Aa n dP B are the tangents to the parabola y^2=4a x , is equally, inclined to the coordinate axes, then the point P lies on the tangent at vertex of the parabola directrix of the parabola circle with center at the origin and radius a the line of the latus rectum.

Find the equation of a curve passing through the point (0, 1) if the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Show that the normal vector to the plane 2x+2y+2z=3 is equally inclined with the coordinate axes.

If the tangent to the curve y = f(x) at the point (x, y) is parallel to the x-axis, then (dy)/(dx) is