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 `y=|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).

Find the equation of a 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.

Let a curve y=f(x) pass through (1,1), at any point p on the curve tangent and normal are drawn to intersect the X-axis at Q and R respectively. If QR = 2 , find the equation of all such possible curves.

If A and B are the points of intersection of y=f(x) and y=f^(-1)(x) , then

Find the equations of the tangent and the normal to the following curves at the given point: y = sin ^2 x at x = pi/2