Question

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

Hint:

### When a point lies in between the lines. Then, the point satisfy that the product of values with respect to lines should be less than zero.

## 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

### Related Questions to study

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Hence the point is (, ).

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### Assertion (A): The lines represented by and x+ y=2 do not form a triangle

Reason (R): The above three lines concur at (1,1)

Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.

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Reason (R): The above three lines concur at (1,1)

Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.

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### P_{1},P_{2},P_{3}, be the product of perpendiculars from (0,0) to respectively then:

P1 = 1;

P2 = ;

P3 = ;

>>> Therefore, we can say that P1>P2>P3.

### P_{1},P_{2},P_{3}, be the product of perpendiculars from (0,0) to respectively then:

P1 = 1;

P2 = ;

P3 = ;

>>> Therefore, we can say that P1>P2>P3.

### If θ is angle between pair of lines , then

>>> = 2.

>>> tan =

>>> = 10.

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>>> = 2.

>>> tan =

>>> = 10.

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Hence, x=y is the the line that is concurrent with the pair of straight lines.

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>>>The point of intersection of the pair of straight lines x^{2} – 5xy + 6y^{2} + x – 3y = 0 is (-3, -1)

### If the equation represents a pair of straight lines then their point of intersection is

>>>The point of intersection of the pair of straight lines x^{2} – 5xy + 6y^{2} + x – 3y = 0 is (-3, -1)