The equation of the radical axis of the pair of circles ` 7x^(2) + 7y^(2) - 7x + 14 y + 18 = 0 " and " 4x^(2) + 4y^(2) - 7x + 8y + 20 = 0 ` is :

Options

A. x - 2y - 5 = 0
B. 2x - y + 5 = 0
C. 21x - 68 = 0
D. 23x - 68 = 0

Answer

C

Explanation

Given circle are,
`S -= 7x^(2) + 7y^(2) - 7x + 14 y + 18 = 0`
`implies S -= x^(2) + y^(2) - x + 2y + (18)/(7) = 0`
`S^(1) -= 4x^(2) + 4y^(2) - 7x + 8y + 20 = 0`
`implies S^(1) -= x^(2) + y^(2) - (7)/(4) x + 2y + 5 = 0`
`implies` Equation of radical axis is `S - S^(1) = 0`
`implies -x + (18)/(7) + (7)/(4) x - 5 = 0`
`implies - 28 x + 72 + 49 x - 140 = 0`
`:. 21 x - 68 = 0`