Coordinate Geometry
Straight Lines
MMTS_Full_Test_21
Grade 12
Question:
If a straight line having negative slope passing through the point $P=(8,2)$ meets the $x$-axis at $A$ and $y$-axis at $B$ respectively. Then the minimum value of $OA+OB$ ($O$ being origin) is
Step-by-Step Solution
Key Concept: Intercept form: $x/a+y/b=1$ passing through $(8,2)$; minimize $a+b$
By AM-GM: $(a+b)\ge(\sqrt{8}+\sqrt{2})^2=18$. Min $OA+OB=18$.
Correct Answer: 2