Equation-of-circle-touching-the-line-x-2-y-3-4-will-be-

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

E q u a t i o n o f c i r c l e t o u c h i n g t h e l i n e

∣ x - 2 ∣ + ∣ y - 3 ∣ = 4 w i l l b e

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

c e n t r e o f c i r c l e i s a p o i n t (2, 3)

w i t h r a d i u s = \frac{∣ 2 + 3 - 9 ∣}{\sqrt{2}} = 2 \sqrt{2}

e q u a t i o n o f c i r c l e i s

{(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)

Missing \left or extra \right

with side equal to 4 \sqrt{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 = \frac{∣ 2 + 3 - 9 ∣}{\sqrt{1^{2} + 1^{2}}} = 2 \sqrt{2} . Thus, the equation

of the circle touches to the graph is

{(x - 2)}^{2} + {(y - 3)}^{2} = 8