Question: All points on the curve y<sup>2</sup> = 4a $\left( x + a\sin\frac{x}{a} \right)$ at which the tan...

Question

All points on the curve y² = 4a $\left( x + a\sin\frac{x}{a} \right)$ at which the

tangents are parallel to the axis of x, lie on a :

Answer 1

y² = 4a(x + a sin $\frac{x}{a}$ ) …….(1)

2y $\frac{dy}{dx}$ = 4a(1 + a. $\frac{1}{a}$ cos $\frac{x}{a}$ ) = 0

Ž cos $\frac{x}{a}$ = – 1, x = nap

From (1) y² = 4a (x + a sin $\frac{na\pi}{a}$ )

at x = nap y² = 4ax parabola

Question: All points on the curve y<sup>2</sup> = 4a \(\left( x + a\sin\frac{x}{a} \right)\) at which the tan...