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현재 위치

Equation of a circle that passes through a point and is tangent to both the x and y axes

작성자 Uploader : airun 작성일 Upload Date: 2019-10-28변경일 Update Date: 2023-09-09조회수 View : 57

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The basic form of the equation of a circle is as follows.

(x-a)^2 + (y-b)^2 = r^2

In this case, the center coordinate of the circle are (a, b) and the radius is r.

Since it is simultaneously tangent to the x-axis and y-axis, in the first quadrant, a = b = r, and the basic equation can be written as follows.

(x-a)^2 + (y-a)^2 = a^2

Also, since it passes through one point P(x1, y1),

(x1-a)^2 + (y1-a)^2 = a^2

It can be adjusted as follows.

x1^2 - 2ax1 + a^2 + y1^2 - 2ay1 + a^2 = a^2

a^2 - 2a(x1+y1) + x1^2 + y1^2 = 0

a = (1/2)*(2*(x1+y1)±(4(x1+y1)^2-4*(x1^2+y1^2))^(1/2))

= (x1+y1)±((x1+y1)^2-(x1^2+y1^2))^(1/2)

It shall be solved under the conditions of a = -b = -r in the second quadrant, a = b = -r in the third quadrant, and a = -b = r in the fourth quadrant.

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1st Step for All

현재 위치

Equation of a circle that passes through a point and is tangent to both the x and y axes

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