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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Question 63513This question is from textbook Precalculus
: 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 This question is from textbook Precalculus

Answer by venugopalramana(3286) About Me  (Show Source):
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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
CENTER IS (1,0)