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. a straight line
B. a circle
C. a parabola
D. an ellipse

Answer

C

Explanation

Given `y^(2)=4a(x+asin(x/a))`……………i
`implies2y(dy)/(dx)=4a(1+cos(x/a))`
Since, tangent is parallel to X-axis
`:. (dy)/(dx)=0 [ :' a!=0]`
`implies1+cos(x/a)impliescos(x/a)=-1=cospi`
`implies x/a=2n pi+-piimpliesx=(2n+-1)pia`
`:.` From Eq. i we get `y^(2)=4ax`