Find the distance between parallel lines

(i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0

(ii) l(x + y) + p = 0 and l (x + y) – r = 0

Asked by Pragya Singh | 2 years ago |  100

##### Solution :-

(i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0

Given:

The parallel lines are 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0.

By using the formula,

The distance (d) between parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by

$$d= \dfrac{|C_1-C_2|}{\sqrt{A^2+B^2}}$$

$$d= \dfrac{|-34-31|}{\sqrt{15^2+8^2}}$$

$$d= \dfrac{|-65|}{\sqrt{225+64}}$$

$$d= \dfrac{65}{\sqrt{289}}$$

The distance between parallel lines is $$\dfrac{65}{17}$$

(ii) l(x + y) + p = 0 and l (x + y) – r = 0

Given:

The parallel lines are l (x + y) + p = 0 and l (x + y) – r = 0.

lx + ly + p = 0 and lx + ly – r = 0

by using the formula,

The distance (d) between parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by

$$d= \dfrac{|p-(-r)|}{\sqrt{l^2+l^2}}$$

$$\dfrac{|p+r|}{\sqrt{2l}}$$

$$\dfrac{|p+r|}{l\sqrt{2}}$$

The distance between parallel lines is $$\dfrac{|p+r|}{l\sqrt{2}}$$

Answered by Abhisek | 2 years ago

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