If an angular bisector of the coordinate axes | vedclass

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

Question

(C) The bisectors of the angle between the coordinate axes are $y = x$ and $y = -x$.Since these lines are part of the pair of lines represented by $x^

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) The bisectors of the angle between the coordinate axes are $y = x$ and $y = -x$.Since these lines are part of the pair of lines represented by $x^2+2axy+3y^2=0$,they must satisfy the equation.Case $1$: Substitute $y = x$ into the equation:$x^2+2ax(x)+3x^2 = 0$$4x^2+2ax^2 = 0$$x^2(4+2a) = 0$Since this holds for all $x$,$4+2a = 0$,which gives $a = -2$.Case $2$: Substitute $y = -x$ into the equation:$x^2+2ax(-x)+3(-x)^2 = 0$$x^2-2ax^2+3x^2 = 0$$4x^2-2ax^2 = 0$$x^2(4-2a) = 0$Since this holds for all $x$,$4-2a = 0$,which gives $a = 2$.The possible values of $a$ are $-2$ and $2$.Therefore,the sum of all possible values of $a$ is $(-2) + 2 = 0$.

If an angular bisector of the coordinate axes is one of the lines of $x^2+2ax y+3y^2=0$,then the sum of all possible values of $a$ is

Similar Questions

If $m_1$ and $m_2$ are the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ satisfying the condition $16h^2 = 25ab$,then $\ldots$.

If the equation $ax^{2} + hxy + by^{2} = 0$ represents a pair of coincident lines,then

The combined equation of a pair of lines passing through the origin and inclined at $60^{\circ}$ and $30^{\circ}$ respectively with the $x$-axis is:

If the slope of one line of the pair of lines $2x^2 + hxy + 6y^2 = 0$ is thrice the slope of the other line,then $h =$

The joint equation of the straight lines $x + y = 1$ and $x - y = 4$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module