The equation of pair of lines joining origin to the points of intersection of `x^2 + y^2 =9` and `x + y = 3`

Options

A. `x^(2) + (3-x)^(2) = 9`
B. `xy = 0`
C. `(3+y)^(2) + y^(2) = 9`
D. `(x-y)^(2) = 9`

Answer

B

Explanation

Given, `x^(2) + y^(2) = 9 " "…(i)`
and `x + y = 3 " "…(ii)`
From Eqs. (i) and (ii), we make a homogenous equation.
`rArr x^(2) + y^(2) = (x+y)^(2)`
`rArr x^(2) + y^(2) = x^(2) + y^(2) + 2xy`
`rArr xy = 0`