Question

find the equation of line perpendicular to the line 6x+5y+2=0 passing through the points (5,2)​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Line is 6x+5y+2=0}$

$\underline{\textsf{To find:}}$

$\textsf{The equation of the line perpendicular to 6x+5y+2=0}$

$\textsf{and passes through (5,2)}$

$\underline{\textsf{Solution:}}$

$\textsf{Concept used:}$

$\textsf{The equation of the line perpendicular to ax+by+c=0 can be}$

$\textsf{put in the form}\;\mathsf{b\,x-a\,y=b\,x_1-a\,y_1}$

$\textsf{The equation of the line perpendicular to 6x+5y+2=0}$

$\textsf{can be put in the form}$

$\mathsf{5x-6y=5\,x_1-6\,y_1}$

$\textsf{It passes through (5,2)}$

$\mathsf{5x-6y=5(5)-6(2)}$

$\mathsf{5x-6y=25-12}$

$\mathsf{5x-6y=13}$

$\implies\boxed{\mathsf{5x-6y-13=0}}$

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Find the equation of the line perpendicular to 2x+3y-6=0 and passing through (-1,1)

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