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Lines of a b c is not as easy as 1 2 3

Source: AMC10B 2017 #10

February 16, 2017
AMCAMC 10AMC 10 B2017 AMC 10Acoordinategeometry2017 AMC 10B

Problem Statement

The lines with equations ax−2y=cax-2y=c and 2x+by=−c2x+by=-c are perpendicular and intersect at (1,−5)(1, -5). What is cc?
<spanclass=′latex−bold′>(A)</span>−13<spanclass=′latex−bold′>(B)</span>−8<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>13<span class='latex-bold'>(A) </span> -13\qquad <span class='latex-bold'>(B) </span> -8\qquad <span class='latex-bold'>(C) </span> 2\qquad <span class='latex-bold'>(D) </span> 8\qquad <span class='latex-bold'>(E) </span> 13
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