WJEC FURTHER PURE MATHEMATICS. Past paper question on further coordinate geometry from FP2 paper

1. Further Coordinate Geometry WJEC FP2 June 2008

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

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

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 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.