Home
Class 12
MATHS
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.
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation (x-alpha)^2+(y-beta)^2=k(l x+m y+n)^2 represents (a) a parabola for k = (l^2+m^2)^(-1) (b) an ellipse for 0 (1^2+m^2)^(-1) (d) a point circle for k=0

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

lim_(xto0) ((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

If mgt1 and ninN , such that 1^(m)+2^(m)+3^(m)+...+n^(m)gtn((n+1)/(k))^(m) Then, k=

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

""^(m)C_(r+1)+ sum_(k=m)^(n)""^(k)C_(r) is equal to :

If m =! n and (m + n)^(-1) (m^(-1) + n^(-1)) = m^(x) n^(y) , show that : x + y + 2 = 0.

For natural numbers m, n if (1-y)^(m)(1+y)^(n) = 1+a_(1)y+a_(2)y^(2) + "……." and a_(1) = a_(2) = 10 , then (m,n) is :