Intercept Form of a Line

Q.

Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes

(i) equal in magnitude and both positive. (ii) equal in magnitude but opposite in sign.

Q.

Is $\frac{0}{5}$ undefined slope or zero slope?

Q.

Find the equation of a line which passes through the point (22, - 6) and is such that the intercept on x-axis exceeds the intercept on y-axis by 5.

Q.

The equation $x^2+k{y}^2+4xy=0$ represents two coincident lines, if $k=$

1. $0$

2. $1$

3. $4$

4. $16$

Q.

Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5:3 by this point.

Q.

A Point On The Straight Line $3x+5y=15$ Which Is Equidistant From The Coordinate Axes Will Lie Only In

1. $1^{st},2^{nd}$ and $4^{th}$quadrants

2. $1^{st}$ and $2^{nd}$quadrants

3. $4^{th}$quadrant

4. $1^{st}$quadrant

Q.

Find the equation of the straight line which passes through the point (-3, 8) and cuts off positive intercepts on the coordinate axes whose sum is 7.

Q. The equation of the line(s) which passes through the point $(3,4)$ and its sum of the intercepts on the axes is 14 is/are

1. $x+y-7=0$
2. $x-y+1=0$
3. $4x+3y-24=0$
4. $4x-3y=0$

Q.

The equation of the locus of the foot of perpendiculars drawn from the origin to the line passing through a fixed point $(a,b)$is

1. $x^2+y^2–ax–by=0$

2. $x^2+y^2+ax+by=0$

3. $x^2+y^2–2ax–2by=0$

4. None of these

Q.

If one of the lines of the pair $a{x}^2+2hxy+b{y}^2=0$ bisects the angle between positive directions of the axes, then $a,b,\text{and}h$ satisfy the relation

1. $a+b=2\left|h\right|$

2. $a+b=-2h$

3. $a–b=2\left|h\right|$

4. ${(a–b)}^2=4h^2$

Q.

The point of intersection of the lines $\frac{\left(x-1\right)}{2}=\frac{\left(y-2\right)}{3}=\frac{\left(z-3\right)}{4}$ and $\frac{\left(x-4\right)}{5}=\frac{\left(y-1\right)}{2}=z$ is

1. $\left(0,0,0\right)$

2. $\left(1,1,1\right)$

3. $\left(-1,-1,-1\right)$

4. $\left(1,2,3\right)$

Q.

Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.

Q.

Find the value(s) of $p$ in the following pair of equations: $-3x+5y=7$ and $2px-3y=1$, if the lines represented by these equations are intersecting at a unique point.

Q. If the sum of reciprocals of intercepts made by a straight line on the co-ordinate axes is a constant $K$, then the line will always pass through the point

1. $(K,\frac{1}{K})$
2. $(\frac{1}{K},\frac{1}{K})$
3. $(\frac{1}{K},K)$
4. $(K,K)$

Q.

The intercept cut off from $y-$axis is twice that from $x-$axis by the line and the line is passing through $\left(1,2\right)$ then its equation is

1. $2x+y=4$

2. $2x+y+4=0$

3. $2x-y=4$

4. $2x-y+4=0$

Q.

Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Q.

The line $2x+3y=12$ meets the x-axis at A and y-axis at B. The line through $(5,5)$ perpendicular to AB meets the x-axis and the line AB at C and E respectively. If O is the origin of coordinates, find the area of figure OCEB.

Q.

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (iv) $x–3y–7=0$ and $3x–3y15=0$.

Q.

If the line $2x+3ay-1=0$ and $3x+4y+1=0$ are mutually perpendicular, then the value of $a$ will be

1. $\frac{1}{2}$

2. $2$

3. $-\frac{1}{2}$

4. None of these

Q.

If the point $(5,2)$ bisects the intercept of a line between the axes, then its equation is

1. $2x-5y=20$

2. $2x+5y=20$

3. $5x+2y=20$

4. $5x-2y=20$

Q.

A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through

1. A fixed point

2. A variable point

3. Origin

4. None of these

Q.

Using vectors, find the area of the $△$ABC with vertices A(1, 2, 3), B (2, -1, 4) and C(4, 5, -1).

Q.

The figure formed by the lines $ax\pm by\pm c=0$ is

1. a rectangle

2. a square

3. none of these

4. a rhombus

Q. If a straight line passing through the point $P(-3,4)$ is such that its intercepted portion between the coordinate axes is bisected at $P$, the its equation is :

1. $4x+3y=0$
2. $x-y+7=0$
3. $4x-3y+24=0$
4. $3x-4y+25=0$

Q.

Find the equation of the line which passes through the point $(3,4)$ and is such that the portion of it intercepted between the axes is divided by the point in the ratio $2:3$.

Q.

The angle between the lines $x\cos \alpha +y\sin \alpha =a$ and $x\sin \beta -y\cos \beta =a$ is

1. $\beta -\alpha$

2. $\mathrm{\pi }+\mathrm{\beta }-\mathrm{\alpha }$

3. $\frac{\mathrm{\pi }}{2}+\mathrm{\beta }-\mathrm{\alpha }$

4. $\frac{\mathrm{\pi }}{2}-\mathrm{\beta }+\mathrm{\alpha }$

Q.

Find the equation of the straight line passing through the point (2, 1) and bisecting the portion of the straight line 3x - 5y = 15 lying between the axes.

Q.

The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane x+2y-5z+9=0 is
[MP PET 1991]

1. 

2. 

3. 

4. 

Q.

Reduce the equation 3 x - 2 y + 6 = 0 to the intercept form and find the x and y intercepts.

Q.

A straight line passes through the point $(\alpha ,\beta )$ and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is $\frac{x}{2\alpha }+\frac{y}{2\beta }=1.$