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

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

Let y=f(x)be curve passing through (1,sqrt3) such that tangent at any point P on the curve lying in the first quadrant has positive slope and the tangent and the normal at the point P cut the x-axis at A and B respectively so that the mid-point of AB is origin. Find the differential equation of the curve and hence determine f(x).

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 tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve 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.

If the tangent at any point P of a curve meets the axis of x in T. Then the curve for which OP=PT,O being the origins is

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

If the plane 2x + 3y + 4z=1 intersects X-axis, Y-axis and Z-axis at the points A, B and C respectively, then the centroid of a Delta ABC is …....