Maths-
General
Easy

Question

# If the point ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....

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## The correct answer is:

### Given That:If the point ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then:>>> The joint equation of the two lines x=2y and x=4y becomes:              u ≡ x - 2y = 0 and v ≡ x - 4y = 0 is              u· v = 0, i.e.,             ( x - 2y )·( x - 4y ) = 0. i.e.,             x² - 4xy - 2xy + 8y² = 0, i.e.,            S(x, y) ≡ x² - 6xy + 8y² = 0.... (1)If the point P(a², a) lies in the interior of the acute angle formed by these lines, then the value of S(x, y) at P( x=a², y=a ) is negative, i.e., >>> S(a², a) ≡ (a²)² - 6(a²)(a) + 8a² < 0          ∴ a² ( a² - 6a + 8 ) < 0          ∴ a² - 6a + 8 < 0          ∴ ( a - 2 )( a - 4 ) < 0>>> Therefore, the range of a is (2,4).

u ≡ x - 2y = 0 and v ≡ x - 4y = 0
>>>    S(x, y) ≡ x² - 6xy + 8y² = 0
>>>     ( a - 2 )( a - 4 ) < 0