Vault Of Euclid

Lines Through a Point at a Given Distance from the Origin

Lines, circles and conics core

Find the equations of the lines through \( (4, -2) \) and at a perpendicular distance of \( 2 \) units from the origin.
analytic-geometrylinesdistance-from-point-to-linepoint-slope-formabsolute-valuequadratic-equationperpendicular-distancealgebraic-manipulationfind-equation-of-line

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What this problem tests

Tests the ability to combine the point-slope form of a line with the point-to-line distance formula, and to solve the resulting algebraic equation involving absolute values and square roots.

This is a standard analytic geometry problem often found in precalculus or early calculus courses.

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