The distance between the two parallel lines y | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given equations of the parallel lines are $2x - y + 7 = 0$ and $2x - y + 5 = 0$.Comparing these with the standard form $Ax + By + C_1 = 0$ and

Vedclass · Accepted Answer

$\frac{2}{\sqrt{5}}$

Vedclass · Answer

(C) The given equations of the parallel lines are $2x - y + 7 = 0$ and $2x - y + 5 = 0$.Comparing these with the standard form $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$,we have $A = 2$,$B = -1$,$C_1 = 7$,and $C_2 = 5$.The formula for the distance $d$ between two parallel lines is given by $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$.Substituting the values,we get $d = \frac{|7 - 5|}{\sqrt{2^2 + (-1)^2}}$.$d = \frac{2}{\sqrt{4 + 1}} = \frac{2}{\sqrt{5}}$.

The distance between the two parallel lines $y = 2x + 7$ and $y = 2x + 5$ is:

Similar Questions

If $2p$ is the length of the perpendicular from the origin to the line $\frac{x}{a} + \frac{y}{b} = 1$,then:

Find the distance between the parallel lines $15x + 8y - 34 = 0$ and $15x + 8y + 31 = 0$.

If the points $(1, 2)$ and $(3, 4)$ lie on opposite sides of the line $3x - 5y + a = 0$,then:

If the point $(a, a)$ lies between the lines $|x + y| = 2$,then

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module