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홈 / 라이브러리 / JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry / AI 플래시카드

What is the equation of the tangent line to the circle $x^2 + y^2 = r^2$ at point $(x_1, y_1)$?

덱 'JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry'의 플래시카드.

정답

$x x_1 + y y_1 = r^2$.

해설

In slope form, the line $y = mx + c$ is tangent to the circle $x^2 + y^2 = r^2$ if and only if $c = \pm r\sqrt{1 + m^2}$.

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