Intercept Form of a Line

Q.

The difference between two numbers is $26$ and one number is three times the other. Find them?

Q.

The equation of the line whose x intercept is 3 and y intercept is -2 is

1. $\frac{x}{3}-\frac{y}{2}=1$

2. $\frac{x}{3}+\frac{y}{2}=1$

3. $\frac{x}{2}+\frac{y}{3}=1$

4. $\frac{x}{2}-\frac{y}{3}=1$

Q. If the length of perpendicular from origin to a line is $6$ units and the line makes an angle of ${30}^{\circ }$ with the positive $y-$axis (anti clockwise), then the equation of line is

1. $\sqrt{3}x-y=12$
2. $\sqrt{3}x+y=12$
3. $x+\sqrt{3}y=12$
4. $x-\sqrt{3}y=12$

Q.

Find the equation of a straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14.

1. x + y = 7

2. 4x + 3y = 24

3. x + y = 14

4. 3x + 4y = 24

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

Q. If the length of perpendicular from origin to a line is $6$ units and the line makes an angle of ${30}^{\circ }$ with the positive $y-$axis (anti clockwise), then the equation of line is

1. $\sqrt{3}x-y=12$
2. $\sqrt{3}x+y=12$
3. $x+\sqrt{3}y=12$
4. $x-\sqrt{3}y=12$

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

Q.

What does a dot product represent?

Q. A line passes through $(2,2)$ and has $x$-intercept and $y$-intercept as $\alpha \text{units}$ and $\beta \text{units}$ respectively. It makes a triangle of area $A$ with co-ordinate axes. Then the quadratic equation whose roots are $\alpha$ and $\beta$ is :
($\alpha >0,\beta >0$)

1. $x^2-2Ax+2A=0$
2. $x^2-Ax+2A=0$
3. $x^2+2Ax+2A=0$
4. $x^2+Ax+2A=0$

Q.

The equation of the straight line which passes through the point (3, 4) and whose intercept on y-axis is twice that on x-axis, is

1. 2x – y = 10

2. x + 2y = 10

3. 2x + y = 10

4. 3x-4y+7=0

Q. The equation(s) of the line(s) which cut-off intercepts on the axes whose sum and product are 1 and -6 respectively, is/are

1. 2x-3y-6 = 0
2. 2x-3y = -6
3. -3x+2y = 6
4. 3x - 2y = 6

Q. If $a,c,b$ are three terms of a geometric progression, then the line $ax+by+c=0$

1. has a fixed direction

2. always passes through a fixed point

3. forms a triangle with the coordinate axes whose area is constant

4. always cuts intercepts on the coordinate axes such that their sum is zero

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. $4x-3y=0$