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If the equation (5x-1)^2+(5y-2)^2=(lambd...

If the equation `(5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2` represents an ellipse, then find values of `lambdadot`

Text Solution

Verified by Experts

Given equaiton is
`(x-(1)/(5))^(2)+(y-(2)/(5))^(2)=(lambda-1)^(2)[(3x+4y-1)/(sqrt(3^(2))+4^(2))]^(2)`
or `underset("Distance between p(x,y)" and S((1)/(5),(2)/(5)))ubrace(sqrt((x-(1)/(5))+(y-(2)/(5))^(2)))=underset(e)ubrace(lambda-1)underset(("distance of "P(x,y) "from line"3x+4y-1=0))ubrace((|3x+4y-1|)/(sqrt(3^(2)+4^(2)))`
Thus, we have
`SP=e*P M,` where `0ltelt1`
`:. o lt|lambda-1|lt1`
`rArr lambda epsi (0,2)- {1}`
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