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Find the length of the latus ractum of the ellipse whose foci are (-2,-3) and (1,2) and one of the directrix is x +y=5

Find the length of the latus ractum of the ellipse whose foci are (-2,-3) and (1,2) and one of the directrix is x +y=5

Grade:12th pass

1 Answers

Arun
25750 Points
3 years ago
Focus:(6,7), directrix:x+y+2=0, e= 
3
​ 
 
1
​ 
 
equation of ellipse:(x−6) 
2
 +(y−7) 
2
 =( 
3
​ 
 
1
​ 
 ) 
2
 ( 
1+1
​ 
 
x+y+2
​ 
 ) 
2
 
⇒6(x 
2
 +y 
2
 +36+49−12x−14y)=x 
2
 +y 
2
 +4+2xy+4x+4y
⇒5x 
2
 +5y 
2
 −2xy−76x−88y+506=0

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