This test uses JavaScript to generate your test and mark it. You therefore need to enable Scripting using the Preferences... item in one of the Menu items for this Browser's window. Once enabled, just Reload (Refresh) this page.

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<=>y – x = 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 y – x – 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