A straight line of negative slope passes through ( 8 , 1 ) and intercepts the positive coordinate axes at A , B ; O is the origin. Match each minimum (optimized independently). Column I: (A) Area of △

Question

A straight line of negative slope passes through $(8, 1)$ and intercepts the positive coordinate axes at $A, B; O$ is the origin. Match each minimum (optimized independently). Column I: (A) Area of $△ A OB$ (B) Length $A B$ (C) $O A + OB$ (D) Perimeter of $△ A OB$ Column II: (p) 26 (q) $55$ (r) $9 + 42$ (s) 16

Column I	Column II
(A) Area of $△ A OB$	(p) 26
(B) Length $A B$	(q) $55$
(C) $O A + OB$	(r) $9 + 42$
(D) Perimeter of $△ A OB$	(s) 16

TestHub · Accepted Answer

8/ a + 1/ b ab min A B min ( a + b ) r ( r − 8 ) 2 + ( r − 1 ) 2 r Equality at a ​ = 1 , a , b > 0. ≥ 32 ⇒ min [ △ A OB ] = 16. = ( 8 2/3 + 1 2/3 ) 3/2 = 5 5 ​ . = ( 8 ​ + 1 ) 2 = 9 + 4 2 ​ . = ( a + b + a 2 + b 2 ​ ) /2 > a > 8. ≥ r 2 ⇒ ( r − 5 ) ( r − 13 ) ≥ 0. ≥ 13 ⇒ P ≥ 26. = 52/5 , b = 13/3. ​

Mathematics - Straight Lines Question with Solution | TestHub

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