Question

A straight line l with negative slope passes through (8,2) and cuts the coordinate axes at P and Q. Find absolute minimum value of 'OP+OQ`` where O is the origin-

Answer 1

Correct Answer - 18
Let the equation of line be (y-2) = m(x-8) where `m lt 0.`
`rArr P-= (8-(2)/(m), 0)" and " Q -=(0 ,2-8m)`
`"Now, "OP+OQ =|8-(2)/(m)| + |2 -8m|`
`= 10+(2)/(-m) + (-8m)`
`ge 10+2sqrt((2)/(-m) xx(-8m)) ge 18`