what locus is represented by xy=0 ?

Question

locus represented by the eq. E1.E2 = 0

Answer 1

E1=0, E2 =0
x=0,y=0
let L1 & L2 be the loci represented by xy = 0
let L be the locus represented by xy =0
L1 = {(x,y) : x=0 } = y-axis
L2 = {(x,y) : y=0 } = x-axis
L =( L1 U L2 ) = coordinate axis.

Answer 2

The locus represented by xy=0 is called the coordinate axis.

Locus means the set of all points defined by xy=0.

In order to answer a question like this, you plot the equation first to get the correct representation. You cannot plot all the points but plotting a few will help you.

Answer 3

A locus is a set of points that satisfy the above condition...

so if xy=0, if x = 0 -inf < y < inf
if y = 0 -inf < x < inf

there can be no other solutions.

Answer 4

L = {(x,y) e R | x = 0 or y = 0}

Answer 5

2) enable x = a + ib and y = c + identity Imaginary element of x + y = 0 => b + d = 0 => b = - d Imaginary element of xy = 0 => advert + bc = 0 => a*(-b) + bc = 0 => b (c - a) = 0 => b = 0 or c = a yet, b = 0 => d = 0 meaning x and y at the instant are not complicated (contradiction) => c - a = 0 => c = a => x = a + ib and y = a - ib => x = conjugate of y answer: c). Edit: while Fred solutions a query, there isn't any want for absolutely everyone to respond to it in any respect. He has replied all your questions ok. He has additionally extra lacking factors to my answer. i could have deleted my answer, yet he did no longer answer Q. 2) replied by me, yet in basic terms elaborated my answer to make it suitable. owing to him for an identical. I additionally learnt from his different solutions.

Answer 6

xy=0 if either x or y is zero.

So the cross represented by the the x- and y-axis is the solution.

Answer 7

the two Cartesian lines (x=0 or/and y=0)

Answer 8

The x-axis and the y-axis.

In layman's language, a gigantic "+" sign.

Answer 9

the coordinate axis

Answer 10

origin