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Find the euation of the circle circumscribing a triangle formed by the lines x+y=6,2x+y=4 and x+2y=5 |
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Answer» Solving given three line the vertices of the TRIANGLE are A(1,2),B(−2,8) and C(7,−1)And let P(a,b) the center of the CIRCLE.Therefore,PA 2 =PB 2 =PC 2 ⇒(a−1) 2 +(b−2) 2 =(a+2) 2 +(b−8) 2 =(a−7) 2 +(b+1) 2 Solving above EQUATIONS we get a= 217 and b= 219 Now radius of the circle is PA= (a−1) 2 +(b−2) 2 = 415 2 + 415 2 Hence equation of required circle is,(x− 217 ) 2 +(y− 219 ) 2 =PA 2 = 415 2 + 415 2 ⇒x 2 +y 2 −17x−19y+50=0hope it will help you |
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