Let y=f(x) be a curve passing through (4,3) such that slope of normal at any point lying in the first quadrant is negative and the normal and tangent at any point P cuts the Y-axis at A and B respectively such that the mid-point of AB is origin, then the number of solutions of y=f(x) and `f=|5-|x||,` 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).

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the slope of line AB

The tangent at any point P on y^2 = 4x meets x-axis at Q, then locus of mid point of PQ will be

Find the equation of a curve passing through (1,1) and whose slope of tangent at a point (x, y) is -(x)/(y) .

The slope of normal to the curve x^(3)=8a^(2)y, a gt 0 at a point in the first quadrant is -(2)/(3) , then point is

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

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

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as (x^2-2y)/x , then the curve also passes through the point

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

A family of curves is such that the slope of normal at any point (x, y) is 2(1-y). The orthogonal trajectories of the given family of curves is