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A straight line with negative slope pass...

A straight line with negative slope passing the point (1, 4) meets the coordinate axes at A and B. The minimum value of OA + OB =

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Verified by Experts

The correct Answer is:
`a to s; " b" to p; " c" to q; " q" to r`
(a)

`OA = 1+4 "cot" theta`
`OB = 4+ "tan" theta`
`OA+OB = 5+4 "cot" theta + "tan" theta`
` ge 5 +2 sqrt(4 "cot" theta " tan" theta)`
`=5+(2 xx 2)=9`
(b)

The reflection of P(4, -1) on y=x is Q (-1, 4). Hence,
`PQ = sqrt((4+1)^(2) + (-1-4)^(2)) = sqrt(50) = 5sqrt(2)`
(c)

`AB = 2sqrt(2)`
`OC = sqrt(2)`
The maximum value of d is
`OF = sqrt(2) + 2sqrt(2)`
`=3sqrt(2)`
(d) The given line is
`x= 4+(1)/(sqrt(2))((y+1)/(sqrt(2)) " or " y=2x-9`
Hence, the intercept made by the x-axis is 9/2.
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