A table of values can be useful to identify coordinate pairs which satisfy the equation.
By substituting the values for x, you can calculate corresponding values for y.
If used correctly, your calculator can be a powerful tool to speed up calculations.

Common misconception

There is only value for $$y$$ for any given value of $$x$$

Pythagoras' theorem on a coordinate grid shows that there are two possible places where the $$y$$-coordinate could be for any given value of $x$$. This is also true for the $$x$$-coordinate for any given value of $$y$$

Keywords

Radius - The radius is any line segment that joins the centre of a circle to its edge.

Making connections is really powerful when learning mathematics. Ensuring pupils understand that the general form $$x^2+y^2=r^2$$ is based upon using Pythagoras' theorem to calculate the length of the radius enables them to see the connection between the equation of a circle and the triangle.

Teacher tip

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Starter quiz

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6 Questions

Q1.

The is any line segment that joins the centre of a circle to its edge.

Correct Answer: radius

Q2.

The value of $$x^2+y^2$$ when $$x=3$$ and $$y=-4$$ is

Correct Answer: 25

Q3.

Solve the equation $$y^2=36$$.

$$y=18$$

Correct answer: $$y=6$$

$$y=0$$

Correct answer: $$y=-6$$

$$y=-18$$

Q4.

Solve the equation $$9+x^2=25$$.

$$x=4$$

$$x=\sqrt{34}$$

$$x=-\sqrt{34}$$

$$x=-4$$

Q5.

Here is a right-angled triangle. The length of the side marked $$r$$ is cm.

Correct Answer: 10

Q6.

Jun is solving the equation $$x^2-2x-15=0$$. Select the correct statements.

Correct answer: The equation factorises to give $$(x+3)(x-5)=0$$

The equation factorises to give $$(x-3)(x+5)=0$$

The equation factorises to give $$(x-3)(x-5)=0$$

The solutions are $$x=3$$, $$x=-5$$

The solutions are $$x=-3$$, $$x=5$$

Exit quiz

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6 Questions

Q1.

Select the general form of the equation of a circle centred at the origin.

$$x^2+y^2=r$$

Correct answer: $$x^2+y^2=r^2$$

$$x+y=r$$

$$x^2-y^2=r$$

$$x^2-y^2=r^2$$

Q2.

Match each equation of a circle to the radius of the circle.

Correct Answer:$$x^2+y^2=16$$,4

Correct Answer:$$x^2+y^2=25$$,5

Correct Answer:$$x^2+y^2-11=25$$,6

Correct Answer:$$x^2+y^2=1$$,1

Correct Answer:$$2x^2+y^2=9 + x^2$$,3

Q3.

Select the coordinates that lie on the circle with equation $$x^2+y^2=100$$.

Correct answer: (6, 8)

Correct answer: (10, 0)

(4, 6)

(12, -2)

Correct answer: (8, -6)

Q4.

What is the equation of this circle?

$$x + y = 4$$

$$x+y=16$$

$$x^2+y^2=4$$

$$x^2+y^2=8$$

Correct answer: $$x^2+y^2=16$$

Q5.

Jun draws a line and a circle on the same pair of axes to solve the equations of the line and circle simultaneously. How many possible solutions are there to the simultaneous equations?

Correct answer: 0

Correct answer: 1

Correct answer: 2

Q6.

Solve the simultaneous equations $$x+y=4$$ and $$x^2+y^2=10$$ .

$$x=0$$ and $$y=4$$

Correct answer: $$x=1$$ and $$y=3$$

$$x=2$$ and $$y=2$$

Correct answer: $$x=3$$ and $$y=1$$

$$x=4$$ and $$y=0$$