Home
Class 12
MATHS
A curve passes through the point (1,(pi)...

A curve passes through the point `(1,(pi)/(6))`. Let, the slope of the curve at each point `(x,y)" be "(y)/(x)+sec((y)/(x)),x gt0`. Then the equation of the curve is

A

`sin((y)/(x))=ln x+(1)/(2)`

B

`"cosec"((y)/(x))=lnx+2`

C

`sec((2y)/(x))=lnx+2`

D

`cos((2y)/(x))=lnx+(1)/(2)`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

A curve passes through the point (3,-4) and the slope of the tangent to the curve at any point (x,y) is (-(x)/(y)) . Find the equation of the curve.

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

A curve passes through the point (5,3) and the product of its slope and ordinate at any point (x,y) is equal to its abscissa. Find the equation of the curve.

The slope of the tangent at (x , y) to a curve passing through a point (2,1) is (x^2+y^2)/(2x y) , then the equation of the curve is

The slope of the tangent to a curve at any point (x,y) is (3y+2x+4)/(4x+6y+5) . If the curve passes through (0,-1), find the equation of the curve.

If the slope of the tangent at (x,y) to a curve passing through the point (2,1) is (x^(2)+y^(2))/(2xy) , then the equation of the curve is-

Find the equation of a curve passing through the point (0,1).If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate(abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

If the gradient of the tangent at any point (x,y) of a curve which passes through the point (1, (pi)/(4)) is {(y)/(x)-sin^(2)((y)/(x))} , then the equation of the curve is-

A curve y=f(x) passes through the point P(1,1). The normal to the curve at P is a(y-1)+(x-1)=0. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, find the equation of the curve.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.