If the lines represented by the equation (p - | vedclass

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

Question

(D) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.For these lines to be mutually pe

Vedclass · Accepted Answer

$p$ and $q$ may have any value

Vedclass · Answer

(D) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.For these lines to be mutually perpendicular,the condition is $a + b = 0$.Comparing the given equation $(p - q)x^2 + 2(p + q)xy + (q - p)y^2 = 0$ with the general equation,we have $a = (p - q)$ and $b = (q - p)$.Substituting these into the condition $a + b = 0$,we get $(p - q) + (q - p) = 0$,which simplifies to $0 = 0$.This identity holds true for all values of $p$ and $q$. Therefore,$p$ and $q$ may have any value.

If the lines represented by the equation $(p - q)x^2 + 2(p + q)xy + (q - p)y^2 = 0$ are mutually perpendicular,then:

Similar Questions

If $ax^2 + 6xy + by^2 - 10x + 10y - 6 = 0$ represents a pair of perpendicular lines,then $|a| =$

If the pair of lines $2x^2 + 3xy + y^2 = 0$ makes angles $\theta_1$ and $\theta_2$ with the positive direction of the $X$-axis,then $|\tan(\theta_1 - \theta_2)| = $

Find the value of $k$,if the angle between the straight lines represented by $2x^2 + 5xy + 3y^2 + 6x + 7y + 4 = 0$ is $\tan^{-1}(k)$.

If the pair of straight lines $9x^2 + axy + 4y^2 + 6x + by - 3 = 0$ represents two parallel lines,then:

Find the angle between the pair of lines represented by the equation $x^2+4xy+y^2=0$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module