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

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

In X-Y plane, the path defined by the equation (1)/(x^(m))+(1)/(y^(m)) +(k)/((x+y)^(n)) =0 , is a hyperbola if m =1, k =- 1, n=0

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

If int(m^((1)/(x)))/(x^(2))dx=k(m^((1)/(x)))+c then k is:

Solution of the differential equation {1/x-(y^2)/((x-y)^2)}dx+{(x^2)/((x-y)^2)-1/y}dy=0 is

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

The equation [(1, x, y)][(1,3,1),(0,2,-1),(0,2,-1)] [(1),(x),(y)]=[0] has

Let (x_0, y_0) be the solution of the following equations: (2x)^(1n2)=(3y)^(1n3) 3^(1nx)=2^(1ny) The x_0 is 1/6 (b) 1/3 (c) 1/2 (d) 6

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that x^(m) y^(n) + (1)/(x^(m)y^(n)) = 2 cos (m alpha + n beta)

Let g(x,y) = (x^(2)y)/(x^(4) + y^(2)) for (x,y) ne (0,0) and f(0,0)=0. (i) Show that lim_((x,y) to (0,0)) g(x,y)=0 along every line y=mx, m in R . (ii) Show that lim_((x,y) to (0,0)) g(x,y) = k/(1+k^(2)) , along every parabola y=kx^(2), k in R{0} .