Home
Class 12
MATHS
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

Text Solution

Verified by Experts

`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)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation sqrt((x-4)^(2)+y^(2))+sqrt((x+4)^(2)+y^(2))=6 represents

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

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

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

Equation sqrt((x-5)^(2)+y^(2))+sqrt((x+5)^(2)+y^(2))=20 represents

The equation sqrt([(x-2)^(2)+y^(2)])+ sqrt([(x+2)^(2)+y^(2)])=4

The equation sqrt({(x-2)^2+y^2})+sqrt({(x+2)^2+y^2})=4 represents