ISI2015-DCG-40

Question

The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) represent

• A. a circle
• B. a parabola
• C. an ellipse
• D. a hyperbola

Comments

A??

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how ?

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Just square and add $x$ and $y$.

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@ankitgupta.1729

Is that correct ??

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but $\theta$ will not be removed.. right ?

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oh Sorry I didn't see properly. I thought there is a "minus" sign in the second question, as that is the popular equation.

Thanks.

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if $y=asin\theta - bcos\theta$ then it will be correct. Here, $\theta$ is a parameter and parametric equation are written here, So we have to eliminate $\theta$ .

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So, what should be the answer finally?

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bhai. don't know..I am not getting any method to eliminate $\theta$ here.

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Yeah but I got.

$x^2  + y^2 = 4ab\sin\theta\cos\theta = 2ab.\sin2\theta$

From here we can do.

What do you think??

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I don't think, we can replace $\theta$ here

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I am feeling the same as well.

I hope the question is correct then.

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@gatecse

Please check this question once. 

Is it typed correctly?