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Geometry: Tangent and Normal to a Circle

The circle with centre C( –4, 5) goes through the point P( –11, 12).
The tangent at P has equation:
y + x + = 0

tickcross


Worked Solution:

The gradient of CP is
12 – 5
---
–11 – (–4)
=
7
---
–7
= –1
The gradient of the tangent is perpendicular to this, i.e. 1
<=> the equation of the tangent at P is y = x + const<=>yx = c
To find c, the tangent goes through P( –11, 12): 1( 12) –1( –11 ) = c<=>c = 23
<=> the equation of the tangent at P is yx – 23 = 0 or any multiple of this equation.


© MEI Produced by Dr Ron Knott, revised 5 August 2004
tom . button [AT] mei . org . uk
Test reference: GeomCircleTanNorm.html?ref=39633