Question Number 115261 by bobhans last updated on 24/Sep/20

Equation of circle touching the line   ∣x−2∣+∣y−3∣ = 4 will be

Answered by john santu last updated on 24/Sep/20

centre of circle is a point (2,3)  with radius = ((∣2+3−9∣)/( (√2))) =2(√2)  equation of circle is   (x−2)^2 +(y−3)^2 =8

Answered by 1549442205PVT last updated on 24/Sep/20

Graph of the function ∣x−2∣+∣y−3∣=4  consists of four segments that four  intersection points are A(−2,3),B(2,7)  C(6,3)^� ,D(2,1)⇒ABCD is a square  with side equal to 4(√2) ,the center is  I(2,3),so the distance from I(2,3) to  each of sides equal to the distance from  I to line y=−x+9 or x+y−9=0,so  R=((∣2+3−9∣)/( (√(1^2 +1^2 ))))=2(√2) .Thus,the equation  of the circle touches to the  graph is  (x−2)^2 +(y−3)^2 =8