The equation sqrt((x-4)^2+(y-2)^2)+sqrt(...

The equation `sqrt((x-4)^2+(y-2)^2)+sqrt((x+4)^2+(y-2)^2)=8` represents a

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The correct Answer is:

`e=(sqrt5)/(2)`

`underset(P(x,y)and A(-4,-2))underset("Distance between")(ubrace(sqrt((x+4)^(2)-(y+2)^(2))))-underset(P(x,y)and B(4,2))underset("Distance between")(ubrace(sqrt((x-4)^(2)+(y-2)^(2))))=8`
So, equation represents hyperbola with foci at `A(-4,-2)` and B(4, 2) .
`2ae=ABsqrt(80)`
Also, 2a = 8
`therefore" "e=(AB)/(8)=(sqrt(80))/(8)=(sqrt5)/(2)`

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