Point of Intersection of Two Lines

Q.

Find the coordinates of the intersection of the lines $2x-3y+1=0$ and $2x+4y+5=0$.

1. ($\frac{19}{14}$, $\frac{4}{7}$)

2. ($\frac{-19}{14}$, $\frac{4}{7}$)

3. ($\frac{19}{14}$, $\frac{-4}{7}$)

4. ($\frac{-19}{14}$, $\frac{-4}{7}$)

Q.

If$L_1=0$ and $L_2=0$ be two intersecting straight lines, the number of points, whose distance from $L_1$ is $2$ units and from$L_2$ is $5$ units is

1. $1$

2. $0$

3. $4$

4. infinite

Q. The line $ax+by=a^2{b}^2$, will meet the x- axis at ____.

1. $(0,a{b}^2)$
2. $(a,b)$
3. $(a{b}^2,0)$
4. $(a^2{b}^2,0)$

Q.

There are n straight lines in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

1. 

2. 

3. 

4. 

Q. The system of equations 3x + 2y + z=6, 3x + 4y + 3z = 14, 6x + 10y + 8z = a, has infinite number of solutions, if a =

1. 8
2. 12
3. 24
4. 36

Q.

The lines $2x+y=2$, $x+2y=1$ and $x+y=1$ pass through the same point.

1. True

2. False

Q. Show that the lines $\overline{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda (3\hat{i}-\hat{j})$ and $\overline{r}=(4\hat{i}-\hat{j})+\mu (2\hat{i}-\widehat{3k})$ intersect. Find their point of intersection.

Q.

The lines $x=4$ and $x=3$ intersect at the origin.

1. False

2. True

Q. Point of intersection of the pair of straight lines represented by the equation $8x^2+3y^2-10xy-10x+8y-3=0$ is

1. $(-5,7)$
2. $(5,7)$
3. $(4,7)$
4. $(-4,7)$

Q.

Among the given options, the point of intersection of the lines $x-y-1=0$, $4x+3y-25=0$ and $2x-3y+1=0$ is

1. $(4,1)$

2. $(4,2)$

3. $(4,3)$

4. $(4,4)$

Q. A line is such that its segment between the axes is bisected at the point $(23,27),$ the product of the intercepts made by the line on the coordinate axes is