What is the set of points (x,y) satisfying the equations `x^(2) + y^(2) = 4 and x+ y =2 `?

Options

A. `{(2,0),(-2,0),(0,2)}`
B. ` {(0,2),(0,-2)}`
C. ` {(0,2),(2,0)}`
D. `{(2,0),(-2,0),(0,2),(0,2)}`

Answer

C

Explanation

The given equations are
`x^(2) + y^(2) = 4 `
` and x+y=2" "` …(ii)
` x^(2) + (2 - x) ^(2) = 4 `
`rArr x^(2) + 4 + x^(2) - -4x=4`
` rArr x^(2) +4+x^(2) = 4 `
`rArr 2x^(2) = 4x`
`rArr x=2`
`" When " x = 2 " then " y= 2 -2=0`
Similarly,
`y^(2) + (2-y)^(2) = 4`
` y^(2) + 4 + y^(2) - 4y = 4`
` rArr y = 2 and x=0`
These equations are satisfied by only (2,0) and (0,2)
Hence , required set is ` {(0,2), (2,0)}`