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

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- 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.

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