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In X-Y plane, the path defined by the eq...

In X-Y plane, the path defined by the equation `(1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0`, is (a) a parabola if `m = (1)/(2), k =- 1, n =0` (b) a hyperbola if `m =1, k =- 1, n=0` (c) a pair of lines if `m = k = n =1` (d) a pair of lines if `m = k =- 1, n =1`

A

a parabola if `m = (1)/(2), k =- 1, n =0`

B

a hyperbola if `m =1, k =- 1, n=0`

C

a pair of lines if `m = k = n =1`

D

a pair of lines if `m = k =- 1, n =1`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
(a) `sqrt(x) + sqrt(y) =1`
`rArr + y+2 sqrt(xy) =1`
`rArr 4xy = (1-x-y)^(2)`
(b) `(1)/(x) +(1)/(y) =1 rArr xy - x - y=0` is a hyperbola
(c ) `(1)/(x) +(1)/(y) + (1)/(x+y) =0`
`rArr x^(2) + 3xy + y^(2) =0`, which is a pair of lines.
(d) `x + y -(1)/(x+y) =0`
`rArr (x+y)^(2) =1`
`rArr x+y = +-1` which is a pair of lines.
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