1.

A partical moves in the x-y plane according to the scheme x = -8 sinπt and y = -2 cos²πt, where t is time. Find the equation of path of the particle.DONT SPAM IF YOU SPAM I WILL REPORT YOUR 25 ANSWERS​

Answer» <html><body><p><img align="absmiddle" alt="\blue{\Large{\boxed{\tt{ \red{Solution:- }}}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cblue%7B%5CLarge%7B%5Cboxed%7B%5Ctt%7B%20%5Cred%7BSolution%3A-%20%7D%7D%7D%7D%7D%20" title="\blue{\Large{\boxed{\tt{ \red{Solution:- }}}}}"/></p><p></p><p><img align="absmiddle" alt="\dashrightarrow" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5Cdashrightarrow" title="\dashrightarrow"/><img align="absmiddle" alt="\tt{y = -&lt;klux&gt;2&lt;/klux&gt;\cos^{2}\pi t}" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%5Ctt%7By%20%3D%20-2%5Ccos%5E%7B2%7D%5Cpi%20t%7D" title="\tt{y = -2\cos^{2}\pi t}"/></p><p><img align="absmiddle" alt="\dashrightarrow" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5Cdashrightarrow" title="\dashrightarrow"/><img align="absmiddle" alt="\tt{y = -2(\cos^{2}\pi t-\sin^{2}\pi t)}" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%5Ctt%7By%20%3D%20-2%28%5Ccos%5E%7B2%7D%5Cpi%20t-%5Csin%5E%7B2%7D%5Cpi%20t%29%7D" title="\tt{y = -2(\cos^{2}\pi t-\sin^{2}\pi t)}"/></p><p><img align="absmiddle" alt="\dashrightarrow" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5Cdashrightarrow" title="\dashrightarrow"/><img align="absmiddle" alt="\tt{y = 1-2\sin^{2}\pi t ---(1)}" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%5Ctt%7By%20%3D%201-2%5Csin%5E%7B2%7D%5Cpi%20t%20---%281%29%7D" title="\tt{y = 1-2\sin^{2}\pi t ---(1)}"/></p><p></p><h2>Now,</h2><p><img align="absmiddle" alt="\dashrightarrow" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%5Cdashrightarrow" title="\dashrightarrow"/><img align="absmiddle" alt="\tt{x = -8\sin\pi t}" class="latex-formula" id="TexFormula9" src="https://tex.z-dn.net/?f=%5Ctt%7Bx%20%3D%20-8%5Csin%5Cpi%20t%7D" title="\tt{x = -8\sin\pi t}"/></p><p><img align="absmiddle" alt="\dashrightarrow" class="latex-formula" id="TexFormula10" src="https://tex.z-dn.net/?f=%5Cdashrightarrow" title="\dashrightarrow"/><img align="absmiddle" alt="\tt{\sin\pi t = \frac{-x}{8}---(2)}" class="latex-formula" id="TexFormula11" src="https://tex.z-dn.net/?f=%5Ctt%7B%5Csin%5Cpi%20t%20%3D%20%5Cfrac%7B-x%7D%7B8%7D---%282%29%7D" title="\tt{\sin\pi t = \frac{-x}{8}---(2)}"/></p><p></p><p>Putting the value of <img align="absmiddle" alt="\sf{eq^{n}}" class="latex-formula" id="TexFormula12" src="https://tex.z-dn.net/?f=%5Csf%7Beq%5E%7Bn%7D%7D" title="\sf{eq^{n}}"/>(2)in <img align="absmiddle" alt="\sf{eq^{n}}" class="latex-formula" id="TexFormula13" src="https://tex.z-dn.net/?f=%5Csf%7Beq%5E%7Bn%7D%7D" title="\sf{eq^{n}}"/> (1)</p><h2>we'll <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a>,</h2><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula14" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{y = - 2 \{1 - 2( \frac{ - x}{8})^{2} \}}" class="latex-formula" id="TexFormula15" src="https://tex.z-dn.net/?f=%5Csf%7By%20%3D%20%20%20-%202%20%5C%7B1%20-%202%28%20%5Cfrac%7B%20-%20x%7D%7B8%7D%29%5E%7B2%7D%20%5C%7D%7D" title="\sf{y = - 2 \{1 - 2( \frac{ - x}{8})^{2} \}}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula16" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{y = - 2(1 - \frac{2x ^{2} }{64})}" class="latex-formula" id="TexFormula17" src="https://tex.z-dn.net/?f=%5Csf%7By%20%3D%20%20-%202%281%20-%20%20%5Cfrac%7B2x%20%5E%7B2%7D%20%7D%7B64%7D%29%7D" title="\sf{y = - 2(1 - \frac{2x ^{2} }{64})}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula18" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{y = - 2 + \frac{4x^{2} }{64}}" class="latex-formula" id="TexFormula19" src="https://tex.z-dn.net/?f=%5Csf%7By%20%3D%20%20-%202%20%2B%20%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B64%7D%7D" title="\sf{y = - 2 + \frac{4x^{2} }{64}}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula20" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{y = \frac{x^2}{16} -2}" class="latex-formula" id="TexFormula21" src="https://tex.z-dn.net/?f=%5Csf%7By%20%3D%20%5Cfrac%7Bx%5E2%7D%7B16%7D%20-2%7D" title="\sf{y = \frac{x^2}{16} -2}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula22" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{\frac{x^2}{16}-2 = 0}" class="latex-formula" id="TexFormula23" src="https://tex.z-dn.net/?f=%5Csf%7B%5Cfrac%7Bx%5E2%7D%7B16%7D-2%20%3D%200%7D" title="\sf{\frac{x^2}{16}-2 = 0}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula24" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{x^2 = 2×16}" class="latex-formula" id="TexFormula25" src="https://tex.z-dn.net/?f=%5Csf%7Bx%5E2%20%3D%202%C3%9716%7D" title="\sf{x^2 = 2×16}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula26" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf{x =\sqrt{32}}" class="latex-formula" id="TexFormula27" src="https://tex.z-dn.net/?f=%5Csf%7Bx%20%3D%5Csqrt%7B32%7D%7D" title="\sf{x =\sqrt{32}}"/></p><p><img align="absmiddle" alt="\green\rightarrowtail" class="latex-formula" id="TexFormula28" src="https://tex.z-dn.net/?f=%5Cgreen%5Crightarrowtail" title="\green\rightarrowtail"/><img align="absmiddle" alt="\sf\boxed{x =\pm4\sqrt{2}}" class="latex-formula" id="TexFormula29" src="https://tex.z-dn.net/?f=%5Csf%5Cboxed%7Bx%20%3D%5Cpm4%5Csqrt%7B2%7D%7D" title="\sf\boxed{x =\pm4\sqrt{2}}"/></p><p></p><h2><u>Iden</u><u>t</u><u>i</u><u>ties used</u>:-</h2><p><img align="absmiddle" alt="\purple\mapsto" class="latex-formula" id="TexFormula30" src="https://tex.z-dn.net/?f=%5Cpurple%5Cmapsto" title="\purple\mapsto"/><img align="absmiddle" alt="\rm{\cos2\theta= \cos^2- \sin^2\theta}" class="latex-formula" id="TexFormula31" src="https://tex.z-dn.net/?f=%5Crm%7B%5Ccos2%5Ctheta%3D%20%5Ccos%5E2-%20%5Csin%5E2%5Ctheta%7D" title="\rm{\cos2\theta= \cos^2- \sin^2\theta}"/></p><p><img align="absmiddle" alt="\purple\mapsto" class="latex-formula" id="TexFormula32" src="https://tex.z-dn.net/?f=%5Cpurple%5Cmapsto" title="\purple\mapsto"/><img align="absmiddle" alt="\rm{\sin^2\theta+\cos^2\theta= 1}" class="latex-formula" id="TexFormula33" src="https://tex.z-dn.net/?f=%5Crm%7B%5Csin%5E2%5Ctheta%2B%5Ccos%5E2%5Ctheta%3D%201%7D" title="\rm{\sin^2\theta+\cos^2\theta= 1}"/></p><p></p><p></p><p></p><p><strong><u>NOTE</u></strong>:- for the <a href="https://interviewquestions.tuteehub.com/tag/figure-987693" style="font-weight:bold;" target="_blank" title="Click to know more about FIGURE">FIGURE</a> you may <a href="https://interviewquestions.tuteehub.com/tag/refer-621103" style="font-weight:bold;" target="_blank" title="Click to know more about REFER">REFER</a> to the attachment.</p><p></p><p>Hope it helps :)</p></body></html>


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