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 at Qdot If P Q 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)dot

Find the equation of the curve passing through (1,0) and which has slope 1+(y)/(x) at (x,y)

If the point 3x+4y-24=0 intersects the X -axis at the point A and the Y -axis at the point B , then the incentre of the triangle OAB , where O is the origin, is

At any point (x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3) . Find the equation of the curve, given that it passes through (-2,1) .

The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axis at A and B , then P is the mid-point of A Bdot The curve passes through the point (1,1). Determine the equation of the curve.

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).

Find the point on the curve where tangents to the curve y^2-2x^3-4y+8=0 pass through (1,2).

Tangent to a curve intercepts the y-axis at a point P A line perpendicular to this tangent through P passes through another point (1,0). The differential equation of the curve is

A normal at any point (x , y) to the curve y=f(x) cuts a triangle of unit area with the axis, the differential equation of the curve is