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현재 위치

Linear equation tangent to a point on a circle

작성자 Uploader : aloha 작성일 Upload Date: 2023-06-27변경일 Update Date: 2023-06-29조회수 View : 88

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Find the linear equation y = m*x + n tangent to a point P(x1, y1) on a circle.

The equation of a circle with center coordinates (a, b) and radius r is:

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

Since the line passing through the center O of the circle and a point P on the circle and the tangent line passing through the point P are orthogonal, the slope m of the tangent line is as follows.

m = -(x1-a)/(y1-b)

Since the tangent line passes through the point P, the equation of the tangent line is:

y-y1 = (-(x1-a)/(y1-b))*(x-x1)

y = -((x1-a)/(y1-b))*x + y1+(x1-a)*x1/(y1-b)

Thus,

n = y1+(x1-a)*x1/(y1-b)

□ input data

▷ slope of equation

▷ y-intercept of equation

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현재 위치

Linear equation tangent to a point on a circle

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