1. ©G Dear2008 – Not to be sold/Free to use
Mathematic
(Preliminary)
Locus and
the Parabola
Tangent and
Normal
Stage 6 - Year 11
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©G Dear2008 – Not to be sold/Free to use

2. To find the equation of the tangent of x2 = 4y at ( 6, 9).
Parabola as a locus
The Tangent
To find the equation of the tangent of x2 = 4y at ( 6, 9).
Tangent
Normal
y = x2 4
Make y the subject
dy = 2x = x dx
Differentiate
to find the gradient.
(x = 6)
m = 6 = 3 2
Find the equation of the tangent
y – y1 = m(x – x1)
3x – y – 9 = 0
y – 9 = 3(x – 6)
y – 9 = 3x – 18
3x – y – 9 = 0

3. To find the equation of the normal of x2 = 4y at ( 6, 9).
Parabola as a locus
Normals
Tangent
Normal
To find the equation of the normal of x2 = 4y at ( 6, 9).
x + 3y – 33 = 0
Gradient of tangent
m = 3
m2 = -1 m1
= -1 3
Gradient of normal
Find the equation of the normal
y – y1 = m(x – x1)
y – 9 = -1(x – 6) 3
-3y + 27 = x – 6
x + 3y – 33 = 0