1.

Let (x,y) be a variable point on the curve `4x^(2)+9y^(2)-8x-36y+15=0`. Then min`(x^(2)-2x+y^(2)-4y+5)+"max"(x^(2)-2x+y^(2)-4y+5)` is-(A) `325/36 ` (B) ` 36/325 ` (C) ` 13/25 ` (D) `25/13 `A. `(325)/(36)`B. `(36)/(325)`C. `(13)/(25)`D. `(25)/(13)`

Answer» Correct Answer - A
`4x^(2)+9y^(2)-8y-36y+15=0`
`4(x^(2)-2y)+9(y^(2)-4y)=-15`
`4(x^(2)-2x+1)+9(y^(2)-4y+4=-15+4+36`
`4(x-1)^(2)+9(y-2)^(2)=25`
`((x-a)^(2))/(((5)/(2))^(2))+((y-2)^(2))/(((5)/(3))^(2))=1`……….(1)
`x^(2)-2x+y^(2)-4y+5`
`(x-1)^(2)+(y-2)^(2)`
min of `((x-1)^(2)+(y-2)^(2))=(25)/(9)`
max of `((x-1)^(2)+(y-2)^(2))=(25)/(4)`
`=(25)/(9)+(25)/(4)=(325)/(36)`


Discussion

No Comment Found

Related InterviewSolutions