InterviewSolution
Saved Bookmarks
| 1. |
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» `PrarrIV, QrarrII, R rarrI,SrarrIII` ![]() `" Area of " DeltaLMN=4sqrt3` `(1)/(2)(2B)(sqrt3b)=4sqrt3` `rArr""b^(2)=4rArrb=2rArr2b=4` Here, `(a)/(b)=cot 30^(@)rArra=sqrt3b rArra=2sqrt3` Now, `b^(2)=a^(2)(E^(2)-1)` `therefore""4=12(e^(2)-1)` `rArr""e^(2)=1+(1)/(3)=(4)/(3)` `rArr""e=(2)/(SQRT3)` `"Distance between foci"=2ae=2xx2sqrt3xx(2)/(sqrt3)=8` `"LENGHT of latus rectum "=(2b^(2))/(a)=(2xx4)/(2sqrt3)=(4)/(sqrt3)` |
|