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

$$Equationofcircletouchingtheline$$$$\mid x-2\mid +\mid y-3\mid =4willbe$$

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

$$centreofcircleisapoint(2,3)$$$$withradius=\frac{\mid 2+3-9\mid }{\sqrt{2}}=2\sqrt{2}$$$$equationofcircleis$$$${(x-2)}^2+{(y-3)}^2=8$$

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

$$\mathrm{Graph}\mathrm{of}\mathrm{the}\mathrm{function}\mid \mathrm{x}-2\mid +\mid \mathrm{y}-3\mid =4$$$$\mathrm{consists}\mathrm{of}\mathrm{four}\mathrm{segments}\mathrm{that}\mathrm{four}$$$$\mathrm{intersection}\mathrm{points}\mathrm{are}\mathrm{A}(-2,3),\mathrm{B}(2,7)$$$$\text{Missing left or extra right}$$$$\mathrm{with}\mathrm{side}\mathrm{equal}\mathrm{to}4\sqrt{2},\mathrm{the}\mathrm{center}\mathrm{is}$$$$\mathrm{I}(2,3),\mathrm{so}\mathrm{the}\mathrm{distance}\mathrm{from}\mathrm{I}(2,3)\mathrm{to}$$$$\mathrm{each}\mathrm{of}\mathrm{sides}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{distance}\mathrm{from}$$$$\mathrm{I}\mathrm{to}\mathrm{line}\mathrm{y}=-\mathrm{x}+9\mathrm{or}\mathrm{x}+\mathrm{y}-9=0,\mathrm{so}$$$$\mathrm{R}=\frac{\mid 2+3-9\mid }{\sqrt{1^2+1^2}}=2\sqrt{2}.\mathrm{Thus},\mathrm{the}\mathrm{equation}$$$$\mathrm{of}\mathrm{the}\mathrm{circle}\mathrm{touches}\mathrm{to}\mathrm{the}\mathrm{graph}\mathrm{is}$$$${(\mathrm{x}-2)}^2+{(\mathrm{y}-3)}^2=8$$

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