A normal is drawn at a point `P(x , y)` of a curve. It meets the x-axis and the y-axis in point `A` AND `B ,` respectively, such that `1/(O A)+1/(O B)` =1, where `O` is the origin. Find the equation of such a curve passing through `(5. 4)`

A normal is drawn at a point P(x,y) of a curve.It meets the x-axis and the y-axis in point A AND B, respectively,such that (1)/(OA)+(1)/(OB)=1, where O is the origin.Find the equation of such a curve passing through (5,4)

A normal is drawn at a point P(x,y) on a curve.It meets the x-axis and thedus ofthe director such that (x intercept) ^(-1)+(y- intercept) ^(-1)=1, where O is origin,the curve passing through (3,3).

A normal is drawn at a point P(x,y) of a curve It meets the x-axis at Q If PQ is of constant length k such a curve passing through (0,k) is

Tangent is drawn at any point P of a curve which passes through (1,1) cutting x -axis and y -axis at A and B respectively.If AP:BP=3:1, then

A normal is drawn at a point P(x,y) of a curve.It meets the x-axis at Q. If PQ has constant length k, then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^(2)-y^(2)). Find the equation of such a curve passing through (0,k).

A line is drawn from a point P(x, y) on the curve y = f(x), making an angle with the x-axis which is supplementary to the one made by the tangent to the curve at P(x, y). The line meets the x-axis at A. Another line perpendicular to it drawn from P(x, y) meeting the y-axis at B. If OA = OB, where O is the origin, theequation of all curves which pass through (1, 1) is

If the length of the sub-normal (projection of that part of the normal which is intercepted between the curve and the x-axis on the x-axis at any point P on the curve is directly proportional to OP^(2), where O is the origin, then form the differential equation of the family of curves and hence find the family of curves