AI generatedAlgebraGCSE Higher

Solving a line and circle simultaneously

Substitute into an origin-centred circle equation.

  • The same pair of values must satisfy both equations.
  • For elimination, multiply every term of an equation by the same number. For substitution, replace a variable by an equal expression.
  • Substitute the final pair into both original equations to check.

Example 1

Find both intersection points.

Substitute this -value into the circle equation.Square 1.Take both square roots to find both -coordinates.Pair each -value with .

Example 2

Find both intersection points.

Substitute this -value into the circle equation.Square 2.Take both square roots to find both -coordinates.Pair each -value with .

Your turn

Question 1

Find both intersection points.

Check answer
Substitute this -value into the circle equation.Square 3.Take both square roots to find both -coordinates.Pair each -value with .
Question 2

Find both intersection points.

Check answer
Substitute this -value into the circle equation.Square 4.Take both square roots to find both -coordinates.Pair each -value with .
Question 3

Find both intersection points.

Check answer
Substitute this -value into the circle equation.Square 5.Take both square roots to find both -coordinates.Pair each -value with .
Question 4

Find both intersection points.

Check answer
Substitute this -value into the circle equation.Square 6.Take both square roots to find both -coordinates.Pair each -value with .
Question 5

Find both intersection points.

Check answer
Substitute this -value into the circle equation.Square 7.Take both square roots to find both -coordinates.Pair each -value with .
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