A variable line L passes through the point (3,5) and intersects the positive coordinate axes at the points A and B . The minimum area of the triangle OAB , where O is the origin, is :

Step-by-step solution

aligned & x a + y b =1 & 3 a + 5 b =1 b= 5 a a-3 , a>3 aligned A= 1 2 a b= 1 2 a 5 a (a-3) = 5 2 a^2 a-3 aligned & = 5 2 ( a ^2-9+9 a -3 ) & = 5 2 ( a +3+ 9 a -3 ) & = 5 2 ( a -3+ 9 a -3 +6 ) 30 aligned