In X-Y plane, the path defined by the equation `(1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0`, isA. 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`

In X-Y plane, the path defined by the equation `(1)/(x^(m))+(1)/(y^(m)

1.	In X-Y plane, the path defined by the equation `(1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0`, isA. 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`
Answer» Correct Answer - 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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In X-Y plane, the path defined by the equation `(1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0`, isA. 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`

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