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AP EAPCET 05-Jul-2022 Shift 1 Paper

Section: Mathematics

Question : 52 of 160

Marks: +1, -0

Which of the following represents a parabola?

$x=4 \cos t, y=4 \sin t$
$x^{2}-2=-2 \cos t, y=\cos^{2}\left(\frac{t}{2}\right)$
$\sqrt{x}=\tan t, \sqrt{y}=\sec t$
$x=\sqrt{1-\sin t}, y=\sin\left(\frac{t}{2}\right)+\cos\left(\frac{t}{2}\right)$

Solution: 👈: Video Solution

From option (a).

x=4 \cos t, y=4 \sin t

x^2=16 \cos^2 t, y^2=16 \sin^2 t

So,

x^2+y^2=16

, so this equation of a circle. From option (b),

x^2-2=-2 \cos t, y=\cos^2 \left(\frac{t}{2}\right)

x^2=2-2 \cos t

.....(i)

y=\frac{1+\cos}{2}

.....(ii)

From Eq. (ii),

\cos t=2y-1

Now,

x^2=2-2 \cos t

x^2=2-2(2y-1) \Rightarrow x^2=2-4y+2

x^2=4-4y

So, this is represent the parabola.

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