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).

Let y= f(x) be a curve which passes through (3,1) and is such that normal at any point on it passes through (1,1). Then y= f(x) describes

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

Let C be a curve y=f(x) passing through M(-sqrt(3),1) such that the y-intercept of the normal at any point P(x,y) on the curve C is equal to the distance of P from the origin.Find curve C

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

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)) .

Curve passing through (0,0) and slope of tangent to any point (x,y) is (x^2-4x+y+8)/(x-2) , then curve also passes through

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.