If $a^2 + b^2 = 25, x^2 + y^2 = 17 $ and ax + by = 8, then what is the value of (ay - bx) ?

33 25 21 19

19

If $a^2 + b^2 = 25, x^2 + y^2 = 17 $ ax + by = 8, then what is the value of (ay - bx) = ? We know that, (ax + by)2 + (ay - bx)2 = (a2 + b2) × ( x2 + y2) = 82 + (ay - bx)2 = 25 × 17 =  (ay - bx)2 = 425 - 64 = 361 = (ay - bx) = \(\sqrt {361}\) = 19