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LetH:(x^(2))/(a^(2))-(y^(2))/(b^(2))=1, where a gt b gt 0, be a hperbola in the xy-plane whose conjugate axis LM subtends and angle of 60^(@) at one of its vertices N. Let the area of the triangle LMN be 4sqrt3. The correct option is : |
Answer» <html><body><p>`PrarrIV, QrarrII, R rarrI,SrarrIII`<br/>`PrarrIV,QrarrIII,R rarrI, SrarrII`<br/>`PrarrIV,QrarrI,R rarrIII, SrarrII`<br/>`PrarrIII, QrarrIV,R rarrII, S rarrI`</p>Solution :<img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CG_C07_E15_005_S01.png" width="80%"/><br/> `" Area of " DeltaLMN=4sqrt3` <br/> `(1)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)(<a href="https://interviewquestions.tuteehub.com/tag/2b-300274" style="font-weight:bold;" target="_blank" title="Click to know more about 2B">2B</a>)(sqrt3b)=4sqrt3` <br/> `rArr""b^(2)=4rArrb=2rArr2b=4` <br/> Here, `(a)/(b)=cot 30^(@)rArra=sqrt3b rArra=2sqrt3` <br/> Now, `b^(2)=a^(2)(<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(2)-1)` <br/> `therefore""4=12(e^(2)-1)` <br/> `rArr""e^(2)=1+(1)/(3)=(4)/(3)` <br/> `rArr""e=(2)/(<a href="https://interviewquestions.tuteehub.com/tag/sqrt3-3056952" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT3">SQRT3</a>)` <br/> `"Distance between foci"=2ae=2xx2sqrt3xx(2)/(sqrt3)=8` <br/> `"<a href="https://interviewquestions.tuteehub.com/tag/lenght-1071520" style="font-weight:bold;" target="_blank" title="Click to know more about LENGHT">LENGHT</a> of latus rectum "=(2b^(2))/(a)=(2xx4)/(2sqrt3)=(4)/(sqrt3)`</body></html> | |