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Question

A straight line passes through the point of intersection x2y2=0 and 2xby6=0 and the origin then the complete set of values of b for which the acute angle between this line and y = 0 is less than 45

A
(,4)(7,)
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B
(,5)(7,)
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C
(,4)(5,7)(7,)
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D
(,4)(4,5)(7,)
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Solution

The correct option is D (,4)(4,5)(7,)
As line passes through the point of intersection of x2y2=0 and 2xby6=0
It can be represented as λ(x2y2)+(2xby6)=0
As it passes through the origin
2λ6=0
λ=3
x+(6b)y=0
16b
As its angle with y = 0 is less than π4
1<16b<1
6b>1or<1b<5orb>7
But b4 (as the lines WON'T intersect)
bϵ(,4)(4,5)(7,)

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