The equation of a curve passing through (1,0) for which the product of the abscissa of a point `P` and the intercept made by a normal at `P` on the x-axis equal twice the square of the radius vector of the point `P` is

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

Find the equation of a curve passing through the point (0, -2) given that at any point (x,y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x .

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 (0,0) and whose differential equation is y' = e^(x) sin x .

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the equation of the line passing through the point (2, – 5) and making an intercept of – 3 on the y-axis.

Find the abscissa of the point on the curve xy=(c+x)^(2) , the normal at which cuts off numerically equal intercepts from the axes of coordinates.

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1 . Find the equation of the curve.

Find the equation of a line which passes through the point (2,3,4) and which has equal intercepts on the axes.