Distance between Parallel Lines

Q.

The distance between the parallel lines 8x+6y+5=0 and 4x+3y-25=0 is

1. 7/3

2. 9/2

3. 11/2

4. 5/4

Q.

Find the ratio in which the line ax + by + c = 0 divides the line segment joining p$(x_1,y_1)$ and Q $(x_2,y_2)$.

You are given t = $\frac{(a{x}_2+b{y}_2+c)}{a{x}_1+b{y}_1+c}$

1. -t

2. t

3. 

4. 

Q. Find the distance between and when: (i) PQ is parallel to the y -axis, (ii) PQ is parallel to the x -axis.

Q.

Solve the following systems of inequalities graphically:

$x+y\le 6,x+y\ge 4$

Q.

The portion of a tangent to a parabola cut off between the directrix and point of contact on the curve subtends _____ degree angle at the focus.

Q. Water is being poured into a conical funnel at a rate of $4{\text{cm}}^3\text{/sec},$ whose semi vertical angle is $\frac{\pi }{6}.$ When slant height is $4\text{cm},$ which of the following(s) is correct

1. Rate of change of slant height $=\frac{2}{\pi \sqrt{3}}\text{cm/sec}$
2. Rate of change of height $=\frac{1}{\pi }\text{cm/sec}$
3. Rate of change of slant height $=\frac{1}{\pi \sqrt{3}}\text{cm/sec}$
4. Rate of change of height $=\frac{2}{\pi \sqrt{3}}\text{cm/sec}$

Q.

If the equation $a{x}^2+2hxy+b{y}^2=0$ has one line as the bisector of angle between the coordinate axes, then

1. 

2. 

3. 

4. 

Q.

The distance between the parallel lines $8x+6y+5=0$ and $4x+3y-25=0$ is

1. 7/3

2. 9/2

3. 11/2

4. 5/4

Q. Find the distance between parallel lines (i) 15 x + 8 y – 34 = 0 and 15 x + 8 y + 31 = 0 (ii) l ( x + y ) + p = 0 and l ( x + y ) – r = 0

Q. The ratio in which the line 3x+4y+2=0 divides the distance between 3x+4y+5=0 and 3x+4y-5=0, is

1. 7 : 3
2. 3 : 7
3. 2 : 3
4. None of these

Q. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

1. 
2. 
3. 
4.