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

Lernkarte aus dem Deck JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry.

Antwort

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

Erklärung

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

Synthetischer Inhalt · Redaktion: Ada