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 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 f=|5-|x||, is

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

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

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 AB. The curve passen through the point (1,1). Determine the equation of the curve.

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.

The slope of the tangent at any point on a curve is lambda times the slope of the line joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

The slope of the tangent any point on a curve is lambda times the slope of the joining the point of contact to the origin. Formulate the differential equation and hence find the equation of the curve.

Let y=f(x) be a curve passing through (1,1) such that the triangle formed by the coordinate axes and the tangent at any point of the curve lies in the first quadrant and has area 2. Form the differential equation and determine all such possible curves.

Find the equation of the 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.