All points on the curve y2-4ax-a sinxa- at which the tangents are parallel to the axis of x- lie on-

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Perpendicular Distance of a Point from a Line

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Question

All points on the curve $y^{2} = 4 a (x + a sin \frac{x}{a})$ , at which the tangents are parallel to the axis of x, lie on?

Circle

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Parabola

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Line

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None of these

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Solution

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y^{2} = 4 a (x + a sin \frac{x}{a})

y^{2} = 4 a (x + a s i n (\frac{x}{a}))

y^{2} = 4 a | x + a sin (x / a) |

\frac{x^{2}}{9} + \frac{y^{2}}{16} \equiv 1

\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1

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