Distance between two parallel lines Ax 1- By 1- C 1-0 and Ax 2- By 2- C 2-0 is-A- -C1-C2-A2-B2B- - A x - By - C - A 2- B 2C- - x 2- x 12- y 2- y 12D- 1-A2-B2

The correct option is A nbsp; nbsp; nbsp; nbsp; ...

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Standard VIII

Mathematics

Introduction to Lines

Distance betw...

Question

Distance between two parallel lines Ax₁ + By₁ + C₁ = 0 and Ax₂ + By₂ + C₂ = 0 is:

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Solution

The correct option is C

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Similar questions

Q. Assertion :The distance between the lines

x^{2} + 6 x y + 9 y^{2} + 4 x + 12 y - 5 = 0

\frac{6}{\sqrt{10}}

Reason: Distance between the lines

a x + b y + c_{1} = 0

a x + b y + c_{2} = 0

is given by

\frac{| c_{1} - c_{2} |}{\sqrt{(a^{2} + b^{2})}}

Parallel lines are obtained for the pair of equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ if

Q. If each pair of equations

a_{1} x^{2} + b_{1} x + c_{1} = 0, a_{2} x^{2} + b_{2} x + c_{2} = 0

and

a_{3} x^{2} + b_{3} x + c_{3} = 0

has a common root, then show that
(i)

\frac{c_{1} a_{2} + c_{2} a_{1}}{c_{1} a_{2} - c_{2} a_{1}} + \frac{a_{1} a_{2} b_{3}}{a_{3} (a_{1} b_{2} - a_{2} b_{1})} = 0

(ii)

{(\frac{a_{1} b_{2} - a_{2} b_{1}}{a_{1} c_{2} - a_{2} c_{1}})}^{2} = \frac{a_{1} a_{2} c_{3}}{c_{1} c_{2} a_{3}}

Find the length of the perpendicular from the point $(x^{1}, y^{1})$ to the straight line Ax + By + C = 0, the axes being inclined at an angle $ω$ , and the equation being written such that C is a negative quantity.

The condition for $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ to be consistent and have a unique solution is

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Distance between two parallel lines Ax1 + By1 + C1 = 0 and Ax2 + By2 + C2 = 0 is:

The correct option is C

Distance between two parallel lines Ax₁ + By₁ + C₁ = 0 and Ax₂ + By₂ + C₂ = 0 is: