How this calculation works
Find the implicit equation of the tangent to a circle at a given point.
THE FORMULA
(x₀−h)(x−x₀)+(y₀−k)(y−y₀)=0A worked example
For centre (1,1) and point (4,5), the tangent is 3x+4y−32=0.
Good to know
The given point must differ from the centre.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the implicit equation of the tangent to a circle at a given point.
The primary result is labeled “Normal x coefficient”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The given point must differ from the centre.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
For centre (1,1) and point (4,5), the tangent is 3x+4y−32=0.
Which rule does this calculator apply?
(x₀−h)(x−x₀)+(y₀−k)(y−y₀)=0