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Edexcel IAL Mathematics P1.1.6 solve simultaneous equations

Most direct questions ask for algebraic intersections: form one equation in x, solve the quadratic or quartic, then substitute back for coordinates.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • Substitute a line equation into a curve to form a single quadratic or quartic.
  • Solve the resulting equation exactly before rejecting irrelevant roots where needed.
  • Substitute x-values back into the line or curve to give full intersection coordinates.

P1.1.6 - Solve simultaneous equations question 1

[Maximum number: 2]
Figure 2

Figure 2

Figure 2 shows a sketch of
- the circle C with centre X(4,-3)
- the line l with equation y=52x−552y=\frac{5}{2} x-\frac{55}{2}

Given that l is the tangent to C at the point N,

Hence find

the coordinates of N,

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