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Maths-

General

Easy

Question

A: The product of the perpendiculars from $open parentheses 2 comma negative 1 close parentheses text to the lines end text 2 x to the power of 2 end exponent plus 6 x y plus y to the power of 2 end exponent equals 0$
B: The product of perpendiculars from (1,1) to the pair of lines $3 x to the power of 2 end exponent plus 10 x y plus 3 y to the power of 2 end exponent minus 28 x minus 28 y plus 49 equals 0$
C: The product of perpendiculars from (0,0) to pair of lines $2 x to the power of 2 end exponent minus 13 x y minus 7 y to the power of 2 end exponent plus x plus 23 y minus 6 equals 0$
D: The square of the distance from (0,0) to the point of intersection of $x to the power of 2 end exponent minus y to the power of 2 end exponent minus x minus 3 y minus 2 equals 0$ Arrange A,B,C,D in ascending order

D, A, B, C
B, C, A, D
A, B, C, D
C, A, B, D

The correct answer is: C, A, B, D

$table row cell A colon fraction numerator open vertical bar a alpha to the power of 2 end exponent plus 2 h alpha beta plus b beta to the power of 2 end exponent close vertical bar over denominator square root of left parenthesis a minus b right parenthesis to the power of 2 end exponent plus 4 h to the power of 2 end exponent end root end fraction end cell row cell B colon fraction numerator open vertical bar a alpha to the power of 2 end exponent plus 2 h alpha beta plus b beta to the power of 2 end exponent plus 2 g alpha plus 2 f beta plus c close vertical bar over denominator square root of left parenthesis a minus b right parenthesis to the power of 2 end exponent plus 4 h to the power of 2 end exponent end root end fraction end cell row cell C colon fraction numerator vertical line c vertical line over denominator square root of left parenthesis a minus b right parenthesis to the power of 2 end exponent plus 4 h to the power of 2 end exponent end root end fraction end cell row cell D colon fraction numerator f to the power of 2 end exponent plus g to the power of 2 end exponent over denominator a to the power of 2 end exponent plus h to the power of 2 end exponent end fraction end cell end table$

Related Questions to study

If the equation $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is

If the equation $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is

$text If end text 3 x to the power of 2 end exponent minus 11 x y plus 10 y to the power of 2 end exponent minus 7 x plus 13 y plus k equals 0$ denotes a pair of straight lines, then the point of intersection of the lines is

$text If end text 3 x to the power of 2 end exponent minus 11 x y plus 10 y to the power of 2 end exponent minus 7 x plus 13 y plus k equals 0$ denotes a pair of straight lines, then the point of intersection of the lines is

The point of intersection of the straight lines represented by $6 x to the power of 2 end exponent plus x y minus 40 y to the power of 2 end exponent minus 35 x minus 83 y plus 11 equals 0$

The point of intersection of the straight lines represented by $6 x to the power of 2 end exponent plus x y minus 40 y to the power of 2 end exponent minus 35 x minus 83 y plus 11 equals 0$

parallel

The product of the perpendicular distances from the point (-2, 3) to the lines $x to the power of 2 end exponent minus y to the power of 2 end exponent plus 2 x plus 1 equals 0 text is end text$

The product of the perpendicular distances from the point (-2, 3) to the lines $x to the power of 2 end exponent minus y to the power of 2 end exponent plus 2 x plus 1 equals 0 text is end text$

The distance between the two lines represented by $8 x to the power of 2 end exponent minus 24 x y plus 18 y to the power of 2 end exponent minus 6 x plus 9 y minus 5 equals 0 text is end text$

The distance between the two lines represented by $8 x to the power of 2 end exponent minus 24 x y plus 18 y to the power of 2 end exponent minus 6 x plus 9 y minus 5 equals 0 text is end text$

The distance between the parallel lines $x to the power of 2 end exponent plus 2 square root of 2 x y plus 2 y to the power of 2 end exponent plus 4 x plus 4 square root of 2 y plus 1 equals 0 text is end text$

The distance between the parallel lines $x to the power of 2 end exponent plus 2 square root of 2 x y plus 2 y to the power of 2 end exponent plus 4 x plus 4 square root of 2 y plus 1 equals 0 text is end text$

parallel

The distance between the parallel lines $9 x to the power of 2 end exponent minus 6 x y plus y to the power of 2 end exponent plus 18 x minus 6 y plus 8 equals 0 text is end text$

The distance between the parallel lines $9 x to the power of 2 end exponent minus 6 x y plus y to the power of 2 end exponent plus 18 x minus 6 y plus 8 equals 0 text is end text$

$text If end text a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents a pair of parallel lines then $square root of fraction numerator g to the power of 2 end exponent minus a c over denominator f to the power of 2 end exponent minus b c end fraction end root equals$

$text If end text a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents a pair of parallel lines then $square root of fraction numerator g to the power of 2 end exponent minus a c over denominator f to the power of 2 end exponent minus b c end fraction end root equals$

The equation of the pair of lines through the point (a, b) and parallel to the coordinate axes is

The equation of the pair of lines through the point (a, b) and parallel to the coordinate axes is

parallel

The equation to the pair of lines through the origin perpendicular to the pair of lines $2 x to the power of 2 end exponent plus 5 x y plus 2 y to the power of 2 end exponent plus 10 x plus 5 y equals 0 text is end text$

The equation to the pair of lines through the origin perpendicular to the pair of lines $2 x to the power of 2 end exponent plus 5 x y plus 2 y to the power of 2 end exponent plus 10 x plus 5 y equals 0 text is end text$

The equation $x to the power of 2 end exponent minus 3 x y plus lambda y to the power of 2 end exponent plus 3 x minus 5 y plus 2 equals 0$ when l is a real number, represents a pair of straight lines. If q is the angle between these lines, then $C o s e c to the power of 2 end exponent invisible function application theta equals$

The equation $x to the power of 2 end exponent minus 3 x y plus lambda y to the power of 2 end exponent plus 3 x minus 5 y plus 2 equals 0$ when l is a real number, represents a pair of straight lines. If q is the angle between these lines, then $C o s e c to the power of 2 end exponent invisible function application theta equals$

The angle between the pair of lines $2 left parenthesis x plus 2 right parenthesis to the power of 2 end exponent plus 3 left parenthesis x plus 2 right parenthesis left parenthesis y minus 2 right parenthesis minus 2 left parenthesis y minus 2 right parenthesis to the power of 2 end exponent equals 0 text is end text$

The angle between the pair of lines $2 left parenthesis x plus 2 right parenthesis to the power of 2 end exponent plus 3 left parenthesis x plus 2 right parenthesis left parenthesis y minus 2 right parenthesis minus 2 left parenthesis y minus 2 right parenthesis to the power of 2 end exponent equals 0 text is end text$

parallel

The angle between the pair of lines $2 x to the power of 2 end exponent plus 5 x y plus 2 y to the power of 2 end exponent plus 3 x plus 3 y plus 1 equals 0 text is end text$

The angle between the pair of lines $2 x to the power of 2 end exponent plus 5 x y plus 2 y to the power of 2 end exponent plus 3 x plus 3 y plus 1 equals 0 text is end text$

$x to the power of 2 end exponent plus k subscript 1 end subscript y to the power of 2 end exponent plus 2 k subscript 2 end subscript y equals a to the power of 2 end exponent$ represents a pair of perpendicular lines if

$x to the power of 2 end exponent plus k subscript 1 end subscript y to the power of 2 end exponent plus 2 k subscript 2 end subscript y equals a to the power of 2 end exponent$ represents a pair of perpendicular lines if

$text The value of end text lambda text with end text vertical line lambda vertical line less than 16 text such that end text$ $2 x to the power of 2 end exponent minus 10 x y plus 12 y to the power of 2 end exponent plus 5 x plus lambda y minus 3 equals 0$ represents a pair of straight lines is

$text The value of end text lambda text with end text vertical line lambda vertical line less than 16 text such that end text$ $2 x to the power of 2 end exponent minus 10 x y plus 12 y to the power of 2 end exponent plus 5 x plus lambda y minus 3 equals 0$ represents a pair of straight lines is

parallel

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