A curve `y=f(x)` has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

Find the equation of a curve passing through the point (1.1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

The perpendicular distance of the point P(3,4) from the Y-axis is

The curve is such that the length of the perpendicular from the origin on the tangent at any point P of the curve is equal to the abscissa of Pdot Prove that the differential equation of the curve is y^2-2x y(dy)/(dx)-x^2=0, and hence find the curve.

Find the distance of point P(x,y) from the origin

If the perpendicular distance of a point A, other than the origin from the plane x + y + z = p is equal to the distance of the plane from the origin, then the coordinates of p are

The length of normal at any point to the curve, y=c cosh(x/c) is

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.

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

Let f(x,y) be a curve in the x-y plane having the property that distance from the origin of any tangent to the curve is equal to distance of point of contact from the y-axis. It f(1,2)=0, then all such possible curves are

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