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The major axis and minor axis of an elli...

The major axis and minor axis of an ellipse are, respectively, `x-2y-5=0 and 2x+y+10=0`. If the end of the latus rectum is (3,4) find focii

A

(5,0)

B

(-7,-6)

C

(-11,-8)

D

(11,3)

Text Solution

Verified by Experts

Foot of perpendicular from one end of latus rectum L(3,4) on major axis which is focus is given by
`(x-3)/(1)=(y-4)/(-2)=(-3(-2(4)-5))/(1^(2)+(-2)^(2))=2` ltbr `:. S(x,y)-=S(5,0)`
Another focus is image of S in the line `2x+y+10=0`
`((x-5)/(2)=(y-0)/(1)=(-2(2(5)+0+10))/(2^(2)+1^(2))=8`
`:. S'(,y) -=S(-11,-8)`
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