A point moves in the plane xy according to the law x-asin- t- y-bcos- t- The particle has a trajectory

The correct option is B elliptic #10; #10; #10; #9; #10; #9; #10; #9; #10; #9; #10; #10; #10; #10; #10; #10; #10;We have ...

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Byju's Answer

Standard XII

Physics

Finding Average Velocity

A point moves...

Question

A point moves in the plane xy according to the law $x = a sin ω t$ , $y = b cos ω t$ . The particle has a trajectory

Hyperbolic

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elliptic

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circular

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straight line

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Solution

The correct option is B elliptic

We have
$x = a sin ω t \Rightarrow \frac{x}{a} = sin ω t$ ..... $(I)$
$y = b cos ω t \Rightarrow \frac{y}{b} = cos ω t$ ..... $(I I)$
square & add $(I)$ and $(I I)$ , We have
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
Which is an equation of ellipse.

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A point moves in the plane xy according to the law x=asinωt, y=bcosωt. The particle has a trajectory

The correct option is B elliptic We have x=asinωt⇒xa=sinωt .....(I)y=bcosωt⇒yb=cosωt .....(II)square & add (I) and (II), We havex2a2+y2b2=1Which is an equation of ellipse.

A point moves in the plane xy according to the law $x = a sin ω t$ , $y = b cos ω t$ . The particle has a trajectory

The correct option is B elliptic

We have
$x = a sin ω t \Rightarrow \frac{x}{a} = sin ω t$ ..... $(I)$
$y = b cos ω t \Rightarrow \frac{y}{b} = cos ω t$ ..... $(I I)$
square & add $(I)$ and $(I I)$ , We have
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
Which is an equation of ellipse.