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

Question

All the 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

2y $\frac{dy}{dx}$ = 4a[1 + a cos $\frac{x}{a}.\frac{1}{a}$ ]

Q $\frac{dy}{dx}$ = 0⇒ 1 + cos x/a = 0 ⇒ x/a = (2n + 1)π

⇒ x = (2n + 1)aπ ; For these value’s of x, sin x/a = 0

∴ all points lie on parabola y² = 4ax

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