If the left hand side of the equation x2 - y 2 + x - 3 y + sec q = 0 can be factorized into two linear factors then the value of q is (a)pie/3 b) 7 pie/6 c) 4 pie / 3 d)5 pie / 6

x² + x + -( y² + 3y) + secq = 0

x² + x +1/4 -1/4 -(y²+3y+9/4 - 9/4) + secq = 0                   

(x+1/2)² - [(y+3/2)² -9/4] + secq - 1/4 = 0

(x+1/2)² - (y+3/2)² + 9/4-1/4+secq = 0

this eq will factorize into two linear factors if the constant term is 0

secq + 2 = 0

cosq = -1/2

q = 2pi/3 , 4pi/3

option c is correct