Find the distance between parallel lines. l(x + y) + p = 0 and l(… - Vidyadip

Question

Find the distance between parallel lines. l(x + y) + p = 0 and l(x + y) - r = 0

✓

Answer

We have the equation,
$\mathrm{l} x+\mathrm{l} y+\mathrm{p}=0$
$\text { and } \mathrm{l} x+\mathrm{l} y-\mathrm{r}=0$
$\text { where } \mathrm{a}=1, \mathrm{~b}=1, \mathrm{c}_1=\mathrm{p} \text { and } \mathrm{c}_2=-\mathrm{r}$
$\therefore$ The distance between two parallel lines
d = $\frac{{\left| {{c_1} - {c_2}} \right|}}{{\sqrt {{a^2} + {b^2}} }}$
$\Rightarrow \frac{{\left| {p + r} \right|}}{{\sqrt {{1^2} + {1^2}} }}$
$\Rightarrow \frac{1}{{\sqrt 2 }}\left| {\frac{{p + r}}{1}} \right|$ units

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from STRAIGHT LINES→STRAIGHT LINES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\cos\alpha+\cos\beta=0\sin\alpha+\sin\beta,$ then prove that $\cos2\alpha+\cos2\beta=-2\cos(\alpha+\beta).$

In a single throw of three dice, find the probability of getting the same number on all the three dice.

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Find the number of people who read exactly one newspaper.

The line through the points (h, 3) and (4, 1) intersects the line 7x - 9y - 19 = 0 at right angle. Find the value of h.

A line passes through $(x_1, y_1)$ and $(h, k)$. If slope of the line is m, show that $k - {y_1} = m(h - {x_1})$.

Find the coordinates of the centre and radius of each of the following circles:$\frac{1}{2}(\text{x}^2+\text{y}^2)+\text{x}\cos\theta+\text{y}\sin\theta-4=0$

Find the equation of a line which makes an angle of $tan^{-1} (3)$ with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-\text{x}-1}{2}$

Prove that: $\cos 4 x=1-8 \sin ^2 x \cos ^2 x$