Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If the equation $a x to the power of 2 end exponent minus 6 x y plus y to the power of 2 end exponent plus b x plus c x plus d equals 0$ represents a pair of lines whose slopes are m and $m squared$ , then value(s) of a is/are -

a = –8
a = 8 or - 27
a = 27
a = –1

hint Hint:

Take $y space equals space m x space a n d space y space equals space m squared x space a s space e q u a t i o n space o f space l i n e s space a n d space m u l t i p l y space t h e m space a n d space s i m p l i f y.$

The correct answer is: a = 8 or - 27

Given equation ; $a x squared minus 6 x y plus y squared plus b x plus c x plus d equals 0$
$L e t space y space equals space m x space a n d space y space equals space m squared x space b e space t h e space l i n e W e space c a n space w r i t e space i t space a s left parenthesis y space minus space m x right parenthesis left parenthesis space y space minus space m squared x right parenthesis space equals space 0 O n space s i m p l i f y i n g rightwards double arrow y squared space minus space m squared x y space minus space m x y space plus space m cubed x squared space equals space 0 rightwards double arrow m cubed x squared space minus left parenthesis m squared space plus space m right parenthesis x y space space plus space y squared space equals space 0 C o m p a r i n g space i t space w i t h space e q u a t i o n space a x squared minus 6 x y plus y squared plus b x plus c x plus d equals 0 a space equals space m cubed space comma space space m squared space plus space m space equals space space 6 space a n d space b comma c space comma d space equals space 0 F r o m space a b o v e rightwards double arrow m squared space plus space m space equals space space 6 space C u b i n g space b o t h space s i d e s rightwards double arrow left parenthesis m squared space plus space m right parenthesis cubed space equals space space 6 to the power of 3 end exponent space rightwards double arrow m to the power of 6 space plus space m cubed space plus space 3 m cubed left parenthesis m space plus space m squared right parenthesis space equals space 216 rightwards double arrow a squared space plus space a space plus space 3 a left parenthesis 6 right parenthesis space equals space 216 space......... space left parenthesis space sin c e space m space plus space m squared space equals space 6 space a n d space a space equals space m cubed right parenthesis rightwards double arrow a squared space plus space 19 a space minus space 216 space space equals space 0 O n space F a c t o r i z i n g rightwards double arrow a squared space plus space 27 a space minus space 8 a space minus space 216 space equals space 0 rightwards double arrow a space equals space 8 space o r space minus 27$

Related Questions to study

The curve passing through the points of intersection of $S subscript 1 end subscript identical to fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction minus 1 equals 0$ and $S subscript 2 end subscript identical to x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 g x plus 2 f y x plus C equals 0$ represents a pair of straight lines which are

The curve passing through the points of intersection of $S subscript 1 end subscript identical to fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction minus 1 equals 0$ and $S subscript 2 end subscript identical to x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 g x plus 2 f y x plus C equals 0$ represents a pair of straight lines which are

The number of divisors of $3 cross times 7 to the power of 3 end exponent comma blank 7 cross times 11 to the power of 2 end exponent$ and $2 cross times 61$ are in

The number of divisors of $3 cross times 7 to the power of 3 end exponent comma blank 7 cross times 11 to the power of 2 end exponent$ and $2 cross times 61$ are in

The equation of perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0) is -

The equation of perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0) is -

parallel

If $fraction numerator 1 over denominator b minus a end fraction plus fraction numerator 1 over denominator b minus c end fraction equals fraction numerator 1 over denominator a end fraction plus fraction numerator 1 over denominator c end fraction a n d b not equal to a plus c comma blank t h e n a comma b comma c$ are in

If $fraction numerator 1 over denominator b minus a end fraction plus fraction numerator 1 over denominator b minus c end fraction equals fraction numerator 1 over denominator a end fraction plus fraction numerator 1 over denominator c end fraction a n d b not equal to a plus c comma blank t h e n a comma b comma c$ are in

An infinite GP has first term $x$ and sum 5, then

An infinite GP has first term $x$ and sum 5, then

Area of a triangle whose vertices are $left parenthesis a c o s invisible function application theta comma b s i n invisible function application theta right parenthesis comma left parenthesis negative a s i n invisible function application theta comma b c o s invisible function application theta right parenthesis text and end text left parenthesis negative a c o s invisible function application theta comma negative b s i n invisible function application theta right parenthesis$ is

Area of a triangle whose vertices are $left parenthesis a c o s invisible function application theta comma b s i n invisible function application theta right parenthesis comma left parenthesis negative a s i n invisible function application theta comma b c o s invisible function application theta right parenthesis text and end text left parenthesis negative a c o s invisible function application theta comma negative b s i n invisible function application theta right parenthesis$ is

parallel

In a geometric progression (GP) the ratio of the sum of the first three terms and first six terms is 125:152 the common ratio is

In a geometric progression (GP) the ratio of the sum of the first three terms and first six terms is 125:152 the common ratio is

The sum of the first and third term of an arithmetic series is 12 and the product of first and second term is 24, then first term is

The sum of the first and third term of an arithmetic series is 12 and the product of first and second term is 24, then first term is

If $fraction numerator a over denominator b plus c end fraction comma fraction numerator b over denominator c plus a end fraction comma fraction numerator c over denominator a plus b end fraction$ are in AP, then

If $fraction numerator a over denominator b plus c end fraction comma fraction numerator b over denominator c plus a end fraction comma fraction numerator c over denominator a plus b end fraction$ are in AP, then

parallel

If $a subscript 1 end subscript comma a subscript 2 end subscript comma a subscript 3 end subscript comma horizontal ellipsis comma a subscript n end subscript$ are the $n$ arithmetic means between $a$ and $b$ , then $2 not stretchy sum from i equals 1 to n of a subscript i end subscript$ equals

If $a subscript 1 end subscript comma a subscript 2 end subscript comma a subscript 3 end subscript comma horizontal ellipsis comma a subscript n end subscript$ are the $n$ arithmetic means between $a$ and $b$ , then $2 not stretchy sum from i equals 1 to n of a subscript i end subscript$ equals

The entries in a two-by-two determinant $open vertical bar table row cell a blank b end cell row cell c blank d end cell end table close vertical bar$ are integers that are chosen randomly and independently, and, for each entry, the probability that the entry is odd is p. If the probability that the value of the determinant is even is 1/ 2, then the value of p, is

The entries in a two-by-two determinant $open vertical bar table row cell a blank b end cell row cell c blank d end cell end table close vertical bar$ are integers that are chosen randomly and independently, and, for each entry, the probability that the entry is odd is p. If the probability that the value of the determinant is even is 1/ 2, then the value of p, is

Statement-I : $Cot to the power of negative 1 end exponent invisible function application open parentheses x close parentheses minus tan to the power of negative 1 end exponent invisible function application open parentheses x close parentheses greater than 0 text for all end text x less than 1$
Statement-II : Graph of $c o t to the power of negative 1 end exponent invisible function application left parenthesis x right parenthesis$ is always above the graph of $t a n to the power of negative 1 end exponent invisible function application left parenthesis x right parenthesis text for all end text x less than 1 text . end text$

Statement-I : $Cot to the power of negative 1 end exponent invisible function application open parentheses x close parentheses minus tan to the power of negative 1 end exponent invisible function application open parentheses x close parentheses greater than 0 text for all end text x less than 1$
Statement-II : Graph of $c o t to the power of negative 1 end exponent invisible function application left parenthesis x right parenthesis$ is always above the graph of $t a n to the power of negative 1 end exponent invisible function application left parenthesis x right parenthesis text for all end text x less than 1 text . end text$

parallel

If $c o s to the power of negative 1 end exponent invisible function application x minus c o s to the power of negative 1 end exponent invisible function application fraction numerator y over denominator 2 end fraction equals alpha comma$ then $4 x to the power of 2 end exponent minus 4 x y c o s invisible function application alpha plus y to the power of 2 end exponent text end text$ is equal to-

If $c o s to the power of negative 1 end exponent invisible function application x minus c o s to the power of negative 1 end exponent invisible function application fraction numerator y over denominator 2 end fraction equals alpha comma$ then $4 x to the power of 2 end exponent minus 4 x y c o s invisible function application alpha plus y to the power of 2 end exponent text end text$ is equal to-

The solution of the equation $2 c o s to the power of negative 1 end exponent invisible function application x equals s i n to the power of negative 1 end exponent invisible function application open parentheses 2 x square root of 1 minus x to the power of 2 end exponent end root close parentheses$

The solution of the equation $2 c o s to the power of negative 1 end exponent invisible function application x equals s i n to the power of negative 1 end exponent invisible function application open parentheses 2 x square root of 1 minus x to the power of 2 end exponent end root close parentheses$

The solution of the inequality $open parentheses tan to the power of negative 1 end exponent invisible function application x close parentheses to the power of 2 end exponent minus 3 t a n to the power of negative 1 end exponent invisible function application x plus 2 greater or equal than 0 text is - end text$

The solution of the inequality $open parentheses tan to the power of negative 1 end exponent invisible function application x close parentheses to the power of 2 end exponent minus 3 t a n to the power of negative 1 end exponent invisible function application x plus 2 greater or equal than 0 text is - end text$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.