Intercept Form of a Line

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 h denote the A.M, k denote G.M of the intercepts made on axes by the lines passing through (1, 1) then (h, k) lies on

1. 
2. 
3. 
4. 

Q.

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

1. 
2. 
3. 
4. 

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. None of these

Q. The locus of the midpoint of the portion between the axes of
$xcos\alpha +ysin\alpha =p,$ where p is a constant, is

1. $x^2+y^2=\frac{4}{p^2}$
2. $x^2+y^2=4p^2$
3. $\frac{1}{x^2}\frac{1}{y^2}=\frac{2}{p^2}$
4. $\frac{1}{x^2}+\frac{1}{y^2}=\frac{4}{p^2}$

Q. Line L has intercepts a and b on the coordinate axes. when the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q. Then,

1. $a^2+b^2=p^2+q^2$
2. $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}+\frac{1}{q^2}$
3. $\frac{1}{a^2}+\frac{1}{p^2}=\frac{1}{b^2}+\frac{1}{q^2}$
4. $a^2+p^2=b^2+q^2$

Q. The equation of the line whose X and Y intercepts are respectively twice and thrice of those by the line 2x+5y = 10, will be .

1. 5x+3y = 30
2. 3x+5y = 30
3. 15x+4y = 60
4. 4x+15y = 60

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 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. 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. $x^2+Ax+2A=0$