AP EAMCET · Maths · Parabola
Which of the following represents a parabola?
- A \(x=4 \cos t, y=4 \sin t\)
- B \(x^2-2=-2 \cos t, y=\cos ^2\left(\frac{t}{2}\right)\)
- C \(\sqrt{x}=\tan t, \sqrt{y}=\sec t\)
- D \(x=\sqrt{1-\sin t}, y=\sin \left(\frac{t}{2}\right)+\cos \left(\frac{t}{2}\right)\)
Answer & Solution
Correct Answer
(B) \(x^2-2=-2 \cos t, y=\cos ^2\left(\frac{t}{2}\right)\)
Step-by-step Solution
Detailed explanation
From option (a). \(\begin{aligned} & x=4 \cos t, y=4 \sin t \\ & x^2=16 \cos ^2 t, y^2=16 \sin ^2 t\end{aligned}\) 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)…
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