Number of values of m for which the lines x + | vedclass

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

Question

(A) For the lines to be concurrent,the determinant of the coefficients must be zero:$\begin{vmatrix} 1 & 1 & -1 \ m - 1 & m^2 - 7 & -5 \ m - 2 & 2m

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) For the lines to be concurrent,the determinant of the coefficients must be zero:$\begin{vmatrix} 1 & 1 & -1 \ m - 1 & m^2 - 7 & -5 \ m - 2 & 2m - 5 & 0 \end{vmatrix} = 0$Expanding along the third row:$-(m - 2) \begin{vmatrix} 1 & -1 \ m^2 - 7 & -5 \end{vmatrix} + (2m - 5) \begin{vmatrix} 1 & -1 \ m - 1 & -5 \end{vmatrix} = 0$$-(m - 2)(-5 + m^2 - 7) + (2m - 5)(-5 + m - 1) = 0$$-(m - 2)(m^2 - 12) + (2m - 5)(m - 6) = 0$$-(m^3 - 6m^2 - 12m + 24) + (2m^2 - 12m - 5m + 30) = 0$$-m^3 + 6m^2 + 12m - 24 + 2m^2 - 17m + 30 = 0$$-m^3 + 8m^2 - 5m + 6 = 0 \implies m^3 - 8m^2 + 5m - 6 = 0$Testing for roots,we find that for $m=3$,the lines are not concurrent because the lines become $x+y-1=0$,$2x+2y-5=0$,and $x+y=0$. The lines $x+y-1=0$ and $x+y=0$ are parallel,so they never intersect. Thus,there are no values of $m$ for which the lines are concurrent.

Number of values of $m$ for which the lines $x + y - 1 = 0$,$(m - 1)x + (m^2 - 7)y - 5 = 0$ and $(m - 2)x + (2m - 5)y = 0$ are concurrent,are

Similar Questions

Statement $(A)$: If $3a - 2b + 5c = 0$,then the line $ax + by + c = 0$ is always concurrent at a point.
Reason $(R)$: If $L_1 = 0$ and $L_2 = 0$ are two lines,then the family of lines $L_1 + \lambda L_2 = 0$ is concurrent at the intersection of $L_1$ and $L_2$.

If the lines $4x + 3y - k = 0$,$2x + y + 3 = 0$,and $3x + 2y + k = 0$ are concurrent,then the perpendicular distance from the point of concurrency of these lines to the line $3x + 4y + 2 = 0$ is

The equation of a line passing through the point of intersection of the lines $x - 2y + 8 = 0$ and $3x - y + 4 = 0$ and passing through the origin is

The value of $k$ such that the lines $2x - 3y + k = 0$,$3x - 4y - 13 = 0$,and $8x - 11y - 33 = 0$ are concurrent,is

Find the equation of the line parallel to the $y-$ axis and passing through the point of intersection of the lines $x-7y+5=0$ and $3x+y=0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module