QJEEM20Maaccd: JEE Main 2020 Mathematics - Class 11 JEEM20Maaccd Solution: If the line, 2x - y + 3 = 0 is at a distance and from the lines …

Question

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If the line, 2x - y + 3 = 0 is at a distance

{1 \over {\sqrt 5 }}

and

{2 \over {\sqrt 5 }}

from the lines 4x - 2y +

\alpha

= 0
and 6x - 3y +

\beta

= 0, respectively, then the sum of all possible values of

\alpha

and

\beta

is :

Accepted Answer

Apply distance between parallel line formula

4x - 2y + \alpha = 0

4x - 2y + 6 = 0

\left| {{{\alpha - 6} \over {25}}} \right| = {1 \over {55}}

|\alpha - 6|\, = 2 \Rightarrow \alpha = 8,4

sum = 12

Again

6x - 3y + \beta = 0

6x - 3y + 9 = 0

\left| {{{\beta - 9} \over {3\sqrt 5 }}} \right| = {2 \over {\sqrt 5 }}

|\beta - 9|\, = 6 \Rightarrow \beta = 15,3

sum = 18

\therefore

Sum of all values of

\alpha

and

\beta

is = 30

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