# SOLUTION: The line {{{x - 2y = -4}}} is tangent to the circle at (0,2). the line {{{y = 2x - 7}}} is tangent to the circle at (3,-1). Find the center of the circle

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 Click here to see ALL problems on Miscellaneous Word Problems Question 63514This question is from textbook Precalculus : The line is tangent to the circle at (0,2). the line is tangent to the circle at (3,-1). Find the center of the circleThis question is from textbook Precalculus Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!The line(L1 SAY) x - 2y = -4 is tangent to the circle at (P SAY )(0,2). the line(l2 SAY) y = 2x - 7 is tangent to the circle at(Q SAY) (3,-1). Find the center of the circle LET THE CENTER OF THE CIRCLE BE (C SAY) (H,K) SLOPE OF CP *SLOPE OF L1 =-1...SINCE RADIUS AT POINT OF CONTACT IS PERPENDICULAR TO TANGENT (K-2)/(H)][1/2]=-1 K-2 = -2H......... 2H+K = 2.............1 SIMILARLY SLOPE OF CQ *SLOPE OF L2 =-1...SINCE RADIUS AT POINT OF CONTACT IS PERPENDICULAR TO TANGENT (K+1)/(H-3)][2]=-1 2K+2 = -H+3......... H+2K = 1.............2 2*EQN.1 - EQN.2 3H=3 H = 1 K= 2-(2*1)=0 CENTRE OF THE CIRCLE IS (1,0)