1. Further Coordinate Geometry
WJEC FP2 June 2008

3. We will use the general equation of a line
Find the gradient of the tangent by differentiating implicitly
Differentiating both sides with respect to x
At the point P x y

4. So the GRADIENT OF THE TANGENT AT POINT P IS
The GRADIENT OF THE NORMAL IS THEREFORE
Because the product of the gradients of
TANGENT and NORMAL is -1

5. QED We will use the general equation of a line
This is the required EQUATION OF THE NORMAL
QED

6. The normal meets the x axis at Q
when y=0 find the x coordinate on the normal
Q is the point

7. R is the midpoint of PQ FIND THE MIDPOINT (THE MIDPOINT) R is
X Coordinate of R
Y Coordinate of R
(THE MIDPOINT) R is

8. To find the LOCUS OF R as p varies we ELIMINATE p
and
SUBSTITUTE
This is the equation of the LOCUS of R as p varies.