If the slope of one line of ax^2+4xy+y^2=0 is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the slopes of the lines be $m$ and $3m$ respectively,which are represented by the equation $ax^2+4xy+y^2=0$.Comparing with $Ax^2+2Hxy+By^2=0$,

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Let the slopes of the lines be $m$ and $3m$ respectively,which are represented by the equation $ax^2+4xy+y^2=0$.Comparing with $Ax^2+2Hxy+By^2=0$,we have $A=a$,$2H=4 \Rightarrow H=2$,and $B=1$.The sum of the slopes is $m+3m = -\frac{2H}{B} = -\frac{4}{1} = -4$.$4m = -4 \Rightarrow m = -1$.The product of the slopes is $m(3m) = \frac{A}{B} = \frac{a}{1} = a$.$3m^2 = a$.Substituting $m = -1$,we get $3(-1)^2 = a \Rightarrow a = 3$.Hence,option $C$ is correct.

If the slope of one line of $ax^2+4xy+y^2=0$ is $3$ times the other,then the value of '$a$' is

Similar Questions

If two sides of a triangle are represented by $x^2 - 7xy + 6y^2 = 0$ and the centroid is $(1, 0)$,then the equation of the third side is

The joint equation of the pair of lines passing through the origin and making an angle of $\frac{\pi}{4}$ with the line $3x + y - 6 = 0$ is

The slopes of the lines represented by $x^2+2 h x y+2 y^2=0$ are in the ratio $1:2$. Then $h$ is equal to:

If one of the lines given by $k x^{2}+x y-y^{2}=0$ bisects the angle between the coordinate axes,then the values of $k$ are

$A$ second degree homogeneous equation in $x$ and $y$ always represents:

Vedclass Test Series

Exam Paper Generator

Online Exam Module