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AQA GCSE · Question 18 · Algebra
A circle has centre O and passes through (0, 6). Write down the equation of the circle.
A circle has centre O and passes through (0, 6). Write down the equation of the circle.
How to approach this question
1. Recall the standard equation for a circle centred at the origin: x² + y² = r².
2. Identify the radius (r) of the circle from the information given. The circle passes through (0, 6) and is centred at the origin (0,0), so the radius is the distance between these points.
3. Calculate r².
4. Substitute the value of r² into the standard equation.
Full Answer
The general equation of a circle with centre at the origin (0,0) is x² + y² = r², where r is the radius.
The centre of the circle is O, which is the origin (0,0).
The circle passes through the point (0, 6). The distance from the centre (0,0) to this point is the radius.
The distance is 6 units. So, r = 6.
Therefore, r² = 6² = 36.
The equation of the circle is x² + y² = 36.
The equation for a circle with its centre at the origin (0, 0) is given by the formula x² + y² = r², where `r` is the radius of the circle.
From the diagram and the text, we can see the centre of the circle is O, the origin.
The circle passes through the point (0, 6). The distance from the centre (0, 0) to any point on the circle is the radius. The distance from (0, 0) to (0, 6) is 6 units.
So, the radius `r` is 6.
The equation requires r², so we calculate r² = 6² = 36.
Substituting this into the standard formula, we get the equation of the circle:
x² + y² = 36.
Common mistakes
✗ Writing x² + y² = 6. You need to use r², not r.
✗ Writing x + y = 6 or x + y = 36. You need the squares of x and y.
✗ Giving the equation for a circle not centred at the origin.
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