Find the equation of the curve in which the subnormal varies as the square of the ordinate.

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 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.

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal (a) is linear (b) is homogeneous of second degree (c) has separable variables (d) is of second order

Find the equation of the curve which passes through the point (4, 3) and the gradient of the tengent to the curve at any point on it is equal to the reciprocal of the ordinate of the point.

Find the equation of a curve passing through the point (-2,3), given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2)) .

Obtain the equation of the curve passing through the point(4,3) and at any point the gradient of the tangent to the curve is the reciprocal of the ordinate of the point.

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. Find the area bounded by curve and x-axis in the fourth quadrant.

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 to the locus of a moving point which is always equidistant from the points (2,-1) and (3,2). What curve does the locus represent ?

Find the equation of the straight line which is tangent at one point and normal at another point of the curve x=3t^(2), y=2t^(3) .