Home
Class 12
MATHS
Let y=f(x)be curve passing through (1,sq...

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).

Text Solution

Verified by Experts

The correct Answer is:
`x+f(x)f'(x)=sqrt(x^(2)+f^(2)(x))andf^(2)(x)=1+2x`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Differential Equations Exerise 7 :|1 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|8 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

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

Find the points on the curve y = x^3 at which the slope of the tangent is equal to the y-coordinate of the point.

Find the point on the curve y = x^2 where the slope of the tangent is equal to the x-coordinate of the point.

The point on the curv3e y = sqrt(4x-3) -1, at which the slope of the tangent is 2/3 , is

Find the equation of normal to the curve, y = .x^3 at the point (1,1).

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.

Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

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

Find the slope of the tangent to the curve y = 3x^2 at the point (1/6, 1/12)