ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6 If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle is

>>> L11 $cross times$ L22 <0
>>> (1+cos $theta$ )² -6sin $theta$ -6sin $theta$ cos $theta$ -3sin $theta$ -3sin $theta$ cos $theta$ +18sin $theta$ ² < 0

If $P open parentheses 1 plus fraction numerator alpha over denominator square root of 2 end fraction comma 2 plus fraction numerator alpha over denominator square root of 2 end fraction close parentheses$ be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is

((1+ $fraction numerator alpha over denominator square root of 2 end fraction$ )+2( $2 plus fraction numerator alpha over denominator square root of 2 end fraction$ ) -1).( $2 left parenthesis 1 plus fraction numerator alpha over denominator square root of 2 end fraction right parenthesis plus 4 left parenthesis 2 plus fraction numerator alpha over denominator square root of 2 end fraction right parenthesis minus 15$ ) < 0

If $P open parentheses 1 plus fraction numerator alpha over denominator square root of 2 end fraction comma 2 plus fraction numerator alpha over denominator square root of 2 end fraction close parentheses$ be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is

maths-

is any point in the interior of the quadrilateral formed by the pair of lines and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is

maths-General

If the point $P open parentheses a squared comma a close parentheses subscript minus$ ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....

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

If the point $P open parentheses a squared comma a close parentheses subscript minus$ ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....

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

Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such $vertical line PA minus PB vertical line$ is maximum is

Hence the point is ( $negative 18 over 5$ , $9 over 5$ ).

Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such $vertical line PA minus PB vertical line$ is maximum is

Hence the point is ( $negative 18 over 5$ , $9 over 5$ ).

Assertion (A): The lines represented by $3 x squared plus 10 x y plus 3 y squared minus 16 x minus 16 y plus 16 equals 0$ 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.

Assertion (A): The lines represented by $3 x squared plus 10 x y plus 3 y squared minus 16 x minus 16 y plus 16 equals 0$ 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.

chemistry-

In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:

chemistry-General

P₁,P₂,P₃, be the product of perpendiculars from (0,0) to $x y plus x plus y plus 1 equals 0 comma x squared minus y squared plus 2 x plus 1 equals 0 comma 2 x squared plus 3 x y minus 2 y squared plus 3 x plus y plus 1 equals 0$ respectively then:

P1 = 1;
P2 = $1 half$ ;
P3 = $fraction numerator 1 over denominator square root of 7 end fraction$ ;
>>> Therefore, we can say that P1>P2>P3.

P₁,P₂,P₃, be the product of perpendiculars from (0,0) to $x y plus x plus y plus 1 equals 0 comma x squared minus y squared plus 2 x plus 1 equals 0 comma 2 x squared plus 3 x y minus 2 y squared plus 3 x plus y plus 1 equals 0$ respectively then:

P1 = 1;
P2 = $1 half$ ;
P3 = $fraction numerator 1 over denominator square root of 7 end fraction$ ;
>>> Therefore, we can say that P1>P2>P3.

If θ is angle between pair of lines $x squared minus 3 x y plus lambda y squared plus 3 x minus 5 y plus 2 equals 0$ , then $cosec squared invisible function application theta equals$

>>> $lambda$ = 2.
>>> tan $theta$ = $1 third$
>>> $cos e c squared theta$ = 10.

If θ is angle between pair of lines $x squared minus 3 x y plus lambda y squared plus 3 x minus 5 y plus 2 equals 0$ , then $cosec squared invisible function application theta equals$

>>> $lambda$ = 2.
>>> tan $theta$ = $1 third$
>>> $cos e c squared theta$ = 10.

If the pair of lines $a x squared plus 2 h x y plus b y squared plus 2 g x plus 2 f y plus c equals 0$ intersect on the x-axis, then 2fgh=

2 f g h = b g 2 + c h 2

If the pair of lines $a x squared plus 2 h x y plus b y squared plus 2 g x plus 2 f y plus c equals 0$ intersect on the x-axis, then 2fgh=

2 f g h = b g 2 + c h 2

If the pair of lines $a x squared plus 2 h x y plus b y squared plus 2 g x plus 2 f y plus c equals 0$ intersect on the x-axis, then ac=

$g squared equals a c$

If the pair of lines $a x squared plus 2 h x y plus b y squared plus 2 g x plus 2 f y plus c equals 0$ intersect on the x-axis, then ac=

$g squared equals a c$

maths-

If the equation $x squared plus p y squared plus q y equals a squared$ represents a pair of perpendicular lines then its point of intersection is

maths-General

If the lines $x squared plus 2 x y minus 35 y squared minus 4 x plus 44 y minus 12 equals 0$ and $5 x plus lambda y minus 8 equals 0$ are concurrent then λ

>>> The value of $lambda$ is 2.

If the lines $x squared plus 2 x y minus 35 y squared minus 4 x plus 44 y minus 12 equals 0$ and $5 x plus lambda y minus 8 equals 0$ are concurrent then λ

>>> The value of $lambda$ is 2.

The equation of the line concurrent with the pair of lines $3 x y minus 2 y squared minus 7 x plus y plus 3 equals 0$ is

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

The equation of the line concurrent with the pair of lines $3 x y minus 2 y squared minus 7 x plus y plus 3 equals 0$ is

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

If the equation $lambda x squared minus 5 x y plus 6 y squared plus x minus 3 y equals 0$ represents a pair of straight lines then their point of intersection is

>>>The point of intersection of the pair of straight lines x² – 5xy + 6y² + x – 3y = 0 is (-3, -1)

If the equation $lambda x squared minus 5 x y plus 6 y squared plus x minus 3 y equals 0$ represents a pair of straight lines then their point of intersection is