The pair of lines represented by 3ax^2 + 5xy | vedclass

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

Question

(A) The general equation of a pair of lines passing through the origin is given by $Ax^2 + 2Hxy + By^2 = 0$.For these lines to be perpendicular,the co

Vedclass · Accepted Answer

Two values of $a$

Vedclass · Answer

(A) The general equation of a pair of lines passing through the origin is given by $Ax^2 + 2Hxy + By^2 = 0$.For these lines to be perpendicular,the condition is that the sum of the coefficients of $x^2$ and $y^2$ must be zero,i.e.,$A + B = 0$.In the given equation $3ax^2 + 5xy + (a^2 - 2)y^2 = 0$,we have $A = 3a$ and $B = a^2 - 2$.Setting $A + B = 0$,we get $3a + a^2 - 2 = 0$,which simplifies to $a^2 + 3a - 2 = 0$.This is a quadratic equation in $a$. The discriminant $D = b^2 - 4ac = (3)^2 - 4(1)(-2) = 9 + 8 = 17$.Since $D > 0$,the quadratic equation $a^2 + 3a - 2 = 0$ has two distinct real roots for $a$.Therefore,the lines are perpendicular to each other for two values of $a$.

The pair of lines represented by $3ax^2 + 5xy + (a^2 - 2)y^2 = 0$ are perpendicular to each other for

Similar Questions

If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines,then $\sqrt{\frac{g^2-ac}{f^2-bc}}$ is equal to

If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$,where $(H^2>A B)$,forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)=$ (in $H^2$)

If $4ab = 3h^2$, then the ratio of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is...

The angle between the lines represented by the equation $x^2 - 2pxy + y^2 = 0$ is

If the angle between the lines represented by the equation $x^2+\lambda xy-y^2 \tan^2 \theta=0$ is $2\theta$,then the value of $\lambda$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module