All points on the curve `y^(2)=4a(x+a" sin"(x)/(a))` at which the tangents are parallel to the axis of x lie on a

Options

A. circle
B. parabola
C. straight line
D. None of these

Answer

B

Explanation

Given `y^(2)=4a[x+a sin (x/a)]`……i
`implies2y (dy)/(dx)=4a[1+cos (x/a)]`……………ii M
If tangent is prallel to X-axis then
`(dy)/(dx)=0 c implies cos (x/a)=-1impliessin(x/a)=sqrt(1-cos^(2)(x/a))=0`
On putting this value in eq. (i) we get
`y^(2)=4a(x+0)impliesy^(2)=4ax`
So all the points on the curve
`y^(2)=4a(x+a"sin"x/a)`
When the tangent is parallel to the X=axis lies on parabola.