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Q . LET F 1 AND F 2 ARE THE FOCI OF THE ELLIPSE - 4x 2 + 9y 2 = 36 AND ‘P’ IS A POINT ON THE ELIPSE SUCH THAT - PF 1 = 2PF 2 , THEN THE AREA OF THE TRIANGLE PF 1 F 2 IS ?

Q . LET F1 AND F2 ARE THE FOCI OF THE ELLIPSE -
         
            4x2 + 9y2 = 36  AND ‘P’ IS A POINT
ON THE ELIPSE SUCH THAT -
     PF1 = 2PF2 , THEN THE AREA OF THE TRIANGLE  PF1F2 IS ?
 

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3 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

4x2+ 9y2= 36
By the definition of ellipse,
PF1+ PF2= 2a
a = 3
PF1+ PF2= 6
PF1= 2PF2
PF2= 2
PF1= 4
F1F2can be easily calculated
F1F2= 2ae
e = \sqrt{1-\frac{4}{9}}
e = \frac{\sqrt{5}}{3}
F1F2= 6e
F_{1}F_{2} = 2\sqrt{5}
Now, we have all 3 sides of triangle. Use Heron’s formula
A = \sqrt{p(p-a)(p-b)(p-c)}
p = \frac{2+4+2\sqrt{5}}{2}
p = 3+\sqrt{5}
Now you can put the value in formula & easily get the area.
Bharat Makkar
34 Points
9 years ago
thank you sir......
Bharat Makkar
34 Points
9 years ago
sir please answer other problems too.......i have tried them multiple times.......atleast provide the hints

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